Embedding property of J-holomorphic curves in Calabi-Yau manifolds for generic J

الأصل · EN

In this paper, we prove that for a generic choice of tame (or compatible) almost complex structures J on a symplectic manifold (M²ⁿ,ω) with n ≥ 3 and with its first Chern class c₁(M,ω) = 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.