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 $n\ge 3$ 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.

The exposition of the paper much improved with some clarifications in the Fredholm setting. The proof of 1-jet evaluation transversality is much clarified by correcting minor error in the Fredholm analysis and making precise the choice of Sobolev norms in the proof. A few more references are added

References in corpus (2)

• Automatic Transversality and Orbifolds of Punctured Holomorphic Curves in Dimension Four
• Floer trajectories with immersed nodes and scale-dependent gluing

Cited by in corpus (2)

• Taubes's proof of the Weinstein conjecture in dimension three
• On finiteness and rigidity of J-holomorphic curves in symplectic three-folds