Jholomorphic curves in a nef class
Abstract
Taubes established fundamental properties of $J$holomorphic subvarieties in dimension 4 in \cite{T1}. In this paper, we further investigate properties of reducible $J$holomorphic subvarieties. We offer an upper bound of the total genus of a subvariety when the class of the subvariety is $J$nef. For a spherical class, it has particularly strong consequences. It is shown that, for any tamed $J$, 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2012
 arXiv:
 arXiv:1210.3337
 Bibcode:
 2012arXiv1210.3337L
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Algebraic Geometry;
 Mathematics  Complex Variables;
 Mathematics  Geometric Topology
 EPrint:
 30 pages. v2 Section 4.3 revised