J-holomorphic curves in a nef class
Symplectic Geometry
2015-07-10 v3 Algebraic Geometry
Complex Variables
Geometric Topology
Abstract
Taubes established fundamental properties of holomorphic subvarieties in dimension 4 in \cite{T1}. In this paper, we further investigate properties of reducible holomorphic subvarieties. We offer an upper bound of the total genus of a subvariety when the class of the subvariety is nef. For a spherical class, it has particularly strong consequences. It is shown that, for any tamed , each irreducible component is a smooth rational curve. We also completely classify configurations of maximal dimension. To prove these results we treat subvarieties as weighted graphs and introduce several combinatorial moves.
Cite
@article{arxiv.1210.3337,
title = {J-holomorphic curves in a nef class},
author = {Tian-Jun Li and Weiyi Zhang},
journal= {arXiv preprint arXiv:1210.3337},
year = {2015}
}
Comments
30 pages. v2 Section 4.3 revised; minor changes elsewhere. v3 mistakes corrected