Michigan Mathematical Journal

L2 Estimates and Vanishing Theorems for Holomorphic Vector Bundles Equipped with Singular Hermitian Metrics

Takahiro Inayama

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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.

Article information

Source
Michigan Math. J., Volume 69, Issue 1 (2020), 79-96.

Dates
Received: 5 January 2018
Revised: 21 October 2019
First available in Project Euclid: 14 November 2019

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1573700740

Digital Object Identifier
doi:10.1307/mmj/1573700740

Mathematical Reviews number (MathSciNet)
MR4071346

Zentralblatt MATH identifier
07208926

Subjects
Primary: 32J25: Transcendental methods of algebraic geometry [See also 14C30]
Secondary: 32L20: Vanishing theorems

Citation

Inayama, Takahiro. $L^{2}$ Estimates and Vanishing Theorems for Holomorphic Vector Bundles Equipped with Singular Hermitian Metrics. Michigan Math. J. 69 (2020), no. 1, 79--96. doi:10.1307/mmj/1573700740. https://projecteuclid.org/euclid.mmj/1573700740


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