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Ohsawa-Takegoshi Extension Theorem for Compact Kähler Manifolds and Applications

  • Junyan Cao
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 21)

Abstract

Our main goal in this article is to prove an extension theorem for sections of the canonical bundle of a weakly pseudoconvex Kähler manifold with values in a line bundle endowed with a possibly singular metric. We also give some applications of our result.

Keywords

Kähler manifolds Ohsawa-Takegoshi extension Singular metric 

Notes

Acknowledgements

I would like to thank H. Tsuji who brought me attention to this problem during the Hayama conference 2013. I would also like to thank M. Păun for pointing out several interesting applications, and a serious mistake in the first version of the article. I would also like to thank J.-P. Demailly and X. Zhou for helpful discussions. Last but not least, I would like to thank the anonymous referee for excellent suggestions about this work.

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Copyright information

© Springer International Publishing AG, a part of Springer Nature 2017

Authors and Affiliations

  1. 1.Institut de Mathématiques de JussieuUniversité Paris 6, Case 247ParisFrance

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