J-Holomorphic Curves in a Nef Class

@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}
}
  • 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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    • 8
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    • 6
    • PDF
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    • 1
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    • 10
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    References

    SHOWING 1-10 OF 10 REFERENCES
    Almost Kähler Forms on Rational 4-Manifolds
    • 9
    • PDF
    Pseudo holomorphic curves in symplectic manifolds
    • 2,024
    • PDF
    Numerical characterization of the Kahler cone of a compact Kahler manifold
    • 276
    • PDF
    The structure of rational and ruled symplectic 4-manifolds
    • 302
    • Highly Influential
    • PDF
    Tamed to compatible: symplectic forms via moduli space integration
    • 23
    • Highly Influential
    • PDF
    Principles of Algebraic Geometry
    • 6,808
    Sikorav, On genericity for holomorphic curves in fourdimensional almost-complex manifolds
    • J. Geom. Anal
    • 1997