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A vanishing theorem of Kollár–Ohsawa type

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Abstract

For proper surjective holomorphic maps from Kähler manifolds to analytic spaces, we give a decomposition theorem for the cohomology groups of the canonical bundle twisted by Nakano semi-positive vector bundles by means of the higher direct image sheaves, by using the theory of harmonic integrals developed by Takegoshi. As an application, we prove a vanishing theorem of Kollár–Ohsawa type by combining the \(L^2\)-method for the \(\overline{\partial }\)-equation.

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Acknowledgments

The author would like to thank Professors Osamu Fujino and Taro Fujisawa for reading the draft and giving useful comments. He is supported by the Grant-in-Aid for Young Scientists (B) \(\sharp \)25800051 from JSPS.

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  1. Mathematical Institute, Tohoku University, 6-3, Aramaki Aza-Aoba, Aoba-ku, Sendai, 980-8578, Japan

    Shin-ichi Matsumura

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  1. Shin-ichi Matsumura
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Correspondence to Shin-ichi Matsumura.

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Matsumura, Si. A vanishing theorem of Kollár–Ohsawa type. Math. Ann. 366, 1451–1465 (2016). https://doi.org/10.1007/s00208-016-1371-8

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  • DOI: https://doi.org/10.1007/s00208-016-1371-8

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