English

Castelnuovo's bound and rigidity in almost complex geometry

Symplectic Geometry 2021-03-16 v2 Differential Geometry

Abstract

This article is concerned with the question of whether an energy bound implies a genus bound for pseudo-holomorphic curves in almost complex manifolds. After reviewing what is known in dimensions other than 6, we establish a new result in this direction in dimension 6; in particular, for symplectic Calabi-Yau 6-manifolds. The proof relies on compactness and regularity theorems for J-holomorphic currents.

Keywords

Cite

@article{arxiv.1809.04731,
  title  = {Castelnuovo's bound and rigidity in almost complex geometry},
  author = {Aleksander Doan and Thomas Walpuski},
  journal= {arXiv preprint arXiv:1809.04731},
  year   = {2021}
}
R2 v1 2026-06-23T04:04:43.746Z