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.

arXiv commentThe 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 (3)

• Hodge integrals and degenerate contributions
• 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