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J-holomorphic curves in a nef class | | Tian-Jun Li
; Weiyi Zhang
; | | Date: |
11 Oct 2012 | | 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. | | Source: | arXiv, 1210.3337 | | Services: | Forum | Review | PDF | Favorites | |
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