@article{Li2012JHolomorphicCI,
title={J-Holomorphic Curves in a Nef Class},
author={Tian-jun Li and W. Zhang},
journal={International Mathematics Research Notices},
year={2012},
volume={2015},
pages={12070-12104}
}

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… CONTINUE READING