Castelnuovo's bound and rigidity in almost complex geometry
Abstract
This article is concerned with the question of whether an energy bound implies a genus bound for pseudoholomorphic 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 CalabiYau 6manifolds. The proof relies on compactness and regularity theorems for Jholomorphic currents.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.04731
 Bibcode:
 2018arXiv180904731D
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Differential Geometry
 EPrint:
 Advances in Mathematics 379 (2021)