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DUAL NAKANO POSITIVITY AND SINGULAR NAKANO POSITIVITY OF DIRECT IMAGE SHEAVES

Part of: Deformations of analytic structures Holomorphic fiber spaces (Co)homology theory

Published online by Cambridge University Press:  25 November 2024

YUTA WATANABE Open the ORCID record for YUTA WATANABE [Opens in a new window]
YUTA WATANABE*
Affiliation:
Department of Mathematics, Faculty of Science and Engineering Chuo University 1-13-27 Kasuga, Bunkyo-ku Tokyo 112-8551 Japan wyuta@math.chuo-u.ac.jp
*
wyuta.math@gamil.com
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Abstract

Let $f:X\to Y$ be a surjective projective map, and let L be a holomorphic line bundle on X equipped with a (singular) semi-positive Hermitian metric h. In this article, by studying the canonical metric on the direct image sheaf of the twisted relative canonical bundles $K_{X/Y}\otimes L\otimes \mathscr {I}(h)$, we obtain that this metric has dual Nakano semi-positivity when h is smooth and there is no deformation by f and that this metric has locally Nakano semi-positivity in the singular sense when h is singular.

Keywords

direct image sheavesNakano positivitysingular Hermitian metricsL2-estimates

MSC classification

Primary: 32L10: Sheaves and cohomology of sections of holomorphic vector bundles, general results
Secondary: 32G05: Deformations of complex structures 14F18: Multiplier ideals

Information

Type
Article
Information
Nagoya Mathematical Journal , Volume 257 , March 2025 , pp. 55 - 78
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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