Castelnuovo-Mumford regularity and Bridgeland stability of points in the projective plane
- Title
- Castelnuovo-Mumford regularity and Bridgeland stability of points in the projective plane
- Authors
- 박준영
- Date Issued
- 2017
- Publisher
- 포항공과대학교
- Abstract
- In this thesis we investigate the relationship between the two invariants,
Castelnuovo-Mumford regularity and Bridgeland stability of points in the pro-
jective plane. The main theorem shows that for some outer Bridgeland walls,
generally one invariant precisely determine the other. This means that in general
the ideal sheaf destabilized along a smaller Bridgeland wall has smaller regularity
than the one destabilized along a larger Bridgeland wall. In the monomial scheme
case, we give a sharp inequality between the two invariants using combinatorial
arguments. Finally for the general case, we prove the inequality which implies
that they are somewhat close to each other.
- URI
- http://postech.dcollection.net/jsp/common/DcLoOrgPer.jsp?sItemId=000002324973
https://oasis.postech.ac.kr/handle/2014.oak/92944
- Article Type
- Thesis
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