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March 2020 L2 Estimates and Vanishing Theorems for Holomorphic Vector Bundles Equipped with Singular Hermitian Metrics
Takahiro Inayama
Michigan Math. J. 69(1): 79-96 (March 2020). DOI: 10.1307/mmj/1573700740

Abstract

We investigate singular hermitian metrics on vector bundles, especially strictly Griffiths positive ones. L2 estimates and vanishing theorems usually require an assumption that the vector bundles are Nakano positive. However, there is no general definition of the Nakano positivity in singular settings. In this paper, we show various L2 estimates and vanishing theorems by assuming that the vector bundle is strictly Griffiths positive and the base manifold is projective.

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Takahiro Inayama. "L2 Estimates and Vanishing Theorems for Holomorphic Vector Bundles Equipped with Singular Hermitian Metrics." Michigan Math. J. 69 (1) 79 - 96, March 2020. https://doi.org/10.1307/mmj/1573700740

Information

Received: 5 January 2018; Revised: 21 October 2019; Published: March 2020
First available in Project Euclid: 14 November 2019

zbMATH: 07208926
MathSciNet: MR4071346
Digital Object Identifier: 10.1307/mmj/1573700740

Subjects:
Primary: 32J25
Secondary: 32L20

Rights: Copyright © 2020 The University of Michigan

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Vol.69 • No. 1 • March 2020
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