A vanishing theorem of Kollár–Ohsawa type

Shin ichi Matsumura

doi:10.1007/s00208-016-1371-8

A vanishing theorem of Kollár–Ohsawa type

Shin ichi Matsumura

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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 L²-method for the ∂¯ -equation.

Original language	English
Pages (from-to)	1451-1465
Number of pages	15
Journal	Mathematische Annalen
Volume	366
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-016-1371-8
Publication status	Published - 2016 Dec 1

Keywords

58A14
Primary 32L20
Secondary 14C30

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10.1007/s00208-016-1371-8

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abstract = "For proper surjective holomorphic maps from K{\"a}hler 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 Koll{\'a}r–Ohsawa type by combining the L2-method for the ∂¯ -equation.",

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author = "Matsumura, {Shin ichi}",

note = "Funding Information: 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) 25800051 from JSPS. Publisher Copyright: {\textcopyright} 2016, Springer-Verlag Berlin Heidelberg.",

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T1 - A vanishing theorem of Kollár–Ohsawa type

AU - Matsumura, Shin ichi

N1 - Funding Information: 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) 25800051 from JSPS. Publisher Copyright: © 2016, Springer-Verlag Berlin Heidelberg.

PY - 2016/12/1

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N2 - 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 L2-method for the ∂¯ -equation.

AB - 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 L2-method for the ∂¯ -equation.

KW - 58A14

KW - Primary 32L20

KW - Secondary 14C30

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VL - 366

SP - 1451

EP - 1465

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3-4

ER -

A vanishing theorem of Kollár–Ohsawa type

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Keywords

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