A Koll\'{a}r-type vanishing theorem

Jingcao Wu

A Koll\'{a}r-type vanishing theorem

Complex Variables 2019-06-20 v2 Algebraic Geometry

Authors: Jingcao Wu

Abstract

Let $f:X\rightarrow Y$ be a smooth fibration between two complex manifolds $X$ and $Y$ , and let $L$ be a pseudo-effective line bundle on $X$ . We obtain a sufficient condition for $R^{q}f_{\ast}(K_{X/Y}\otimes L)$ to be reflexive and hence derive a Koll\'{a}r-type vanishing theorem.

Keywords

vanishing theorem vector bundles and cohomology nef and ample line bundles

Cite

@article{arxiv.1906.07350,
  title  = {A Koll\'{a}r-type vanishing theorem},
  author = {Jingcao Wu},
  journal= {arXiv preprint arXiv:1906.07350},
  year   = {2019}
}

Comments

11 pages, accepted for publication in Mathematische Zeitschrift; added references for Introduction

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