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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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