Bounded Negativity and Symplectic 4-Manifolds

Josef G. Dorfmeister

Bounded Negativity and Symplectic 4-Manifolds

Symplectic Geometry 2016-02-11 v2 Algebraic Geometry

Authors: Josef G. Dorfmeister

Abstract

Let $(M,\omega)$ be a symplectic 4-manifold of negative Kodaira dimension. Let $C$ be an $\omega$ -symplectic curve, $J$ -holomorphic for some $J$ tamed by $\omega$ . Then $[C]^2$ is bounded below by a constant depending only on $\omega$ . Related bounded negativity problems for other structures are also briefly discussed. In particular, the symplectic result implies the bounded negativity conjecture for complex projective surfaces with Kodaira dimension $\kappa=-\infty$ .

Keywords

symplectic geometry smooth 4-manifolds algebraic curves

Cite

@article{arxiv.1601.01202,
  title  = {Bounded Negativity and Symplectic 4-Manifolds},
  author = {Josef G. Dorfmeister},
  journal= {arXiv preprint arXiv:1601.01202},
  year   = {2016}
}

Comments

21 pages, This paper has been withdrawn. I thank Weiwei Wu for pointing out a crucial gap in the cutting procedure preceding Theorem 4.2

Bounded Negativity and Symplectic 4-Manifolds

Abstract

Keywords

Cite

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