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

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

2008-05-23

arxiv.org/abs/0805.3581v3

Asian J. Math. 13 (2009), 323 - 340

Mathematics

Symplectic Geometry

The exposition of the paper much improved with some clarifications in the Fredholm setting. The proof of 1-jet evaluation tran

Scientific paper

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 $n \geq 3$ 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 \emph{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.

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