J-holomorphic 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.

30 pages. v2 Section 4.3 revised; minor changes elsewhere. v3 mistakes corrected

References in corpus (2)

• Nongeneric J-holomorphic curves and singular inflation
• Almost Kahler forms on rational 4-manifolds

Cited by in corpus (3)

• Nongeneric J-holomorphic curves and singular inflation
• Almost Kahler forms on rational 4-manifolds
• The curve cone of almost complex 4-manifolds