J-Holomorphic Curves in a Nef Class

  title={J-Holomorphic Curves in a Nef Class},
  author={Tian-jun Li and W. Zhang},
  journal={International Mathematics Research Notices},
  • Tian-jun Li, W. Zhang
  • Published 2012
  • Mathematics
  • International Mathematics Research Notices
  • 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
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