Castelnuovo's bound and rigidity in almost complex geometry
arXiv:1809.04731 · doi:10.1016/j.aim.2020.107550
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.
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- Lectures on Symplectic Field Theory
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- Counting embedded curves in symplectic 6-manifolds