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arXiv · 0805.3581

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

Yong-Geun Oh·Ke Zhu
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Abstract

In this paper, we prove that for a generic choice of tame (or compatible) almost complex structures $J$ on a symplectic manifold $(M^{2n},ω)$ with $n \geq 3$ and with its first Chern class $c_1(M,ω) = 0$, 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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Yong-Geun Oh, Ke Zhu. 2009-02-04. Embedding property of $J$-holomorphic curves in Calabi-Yau manifolds for generic $J$. https://arxiv.org/abs/0805.3581

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