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arXiv · 1210.3337

J-holomorphic curves in a nef class

Tian-Jun Li·Weiyi Zhang
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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.

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Tian-Jun Li, Weiyi Zhang. 2012-10-11. J-holomorphic curves in a nef class. https://arxiv.org/abs/1210.3337

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