EMBEDDING PROPERTY OF J-HOLOMORPHIC CURVES IN CALABI-YAU MANIFOLDS FOR GENERIC J

Abstract

In this paper, we prove that for a generic choice of tame ( or compatible) almost complex structures J on a symplectic manifold (M(2n), omega) with n >= 3 and with its first Chern class c(1) (M, omega) = 0, all somewhere injective J-holomorphic maps from any closed smooth Riemann surface into M are embedded. We derive this result as a consequence of the general optimal 1-jet evaluation transversality result of J-holomorphic maps in general symplectic manifolds that we also prove in this paper.