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PARK, JIHUN (박지훈)

Dept of Mathematics(수학과)

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SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||SURFACES:5||FIBRATIONS:3||MANIFOLDS:2||del Pezzo surface:2||RANK ONE:2||KAHLEREINSTEIN METRICS:2||RATIONALPOINTS:2||KahlerEinstein metric:2||STABILITY:1||del Pezzo fibrations:1||BIRATIONAL MAPS:1||Exceptional singularity:1||BOUNDS:1||Fano threefolds:1||K3 surfaces:1||cylinder:1||birational maps:1||del Pezzo surfaces:1||elliptic fibration:1||nodal hypersurface:1||integral homology:1||THEOREM:1||LINEARSYSTEMS:1||Alphainvariant of Tian:1||Weighted hypersurface:1||Weakly exceptional singularity:1||EXISTENCE:1||Quantum algorithms:1||SINGULARITIES:1||anticanonical divisors:1||ABELIANVARIETIES:1||factoriality:1||THREEFOLDS:1||Halphen pencils:1||Affine cone:1||Anticanonical linear system:1||BIRATIONAL GEOMETRY:1||number field:1||FIELDS:1||Global log canonical threshold:1||Exceptional Fano variety:1||Procrustes problem:1||alphainvariant:1||log canonical threshold:1||perfect field of characteristic 5:1||basepointfreeness:1||Weakly exceptional Fano variety:1||Weighted hypersurfaces:1||log canonical singularity:1||sextic double solid:1||NODES:1||POSITIVE SCALAR CURVATURE:1||LOG CANONICAL THRESHOLDS:1||Birational automorphisms:1||Fano variety:1||KAHLERMETRICS:1||potential density:1||anticanonical divisor:1||G(a)action:1||Log canonical threshold:1||COMPLETEINTERSECTIONS:1||effective anticanonical divisor:1||log canonical thresholds:1||Del Pezzo orbifold:1||ALGORITHMS:1||

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