A Kollár-type vanishing theorem

  • Jingcao WuEmail author


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 \(R^{q}f_{*}(K_{X/Y}\otimes L)\) to be reflexive and hence derive a Kollár-type vanishing theorem.

Mathematics Subject Classification

Primary 32J25 Secondary 32L05 



The author sincerely thanks his supervisor Professor Jixiang Fu for discussions. Thanks also go to Shin-ichi Matsumura, who kindly provided some comments about the references of this paper. Finally, he is very grateful to the referee for many useful suggestions on how to improve the paper.


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Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China

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