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arXiv · 2004.05798

Nakano positivity of singular Hermitian metrics and vanishing theorems of Demailly-Nadel-Nakano type

Takahiro Inayama
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Abstract

In this article, we propose a definition of Nakano semi-positivity of singular Hermitian metrics on holomorphic vector bundles. By using this positivity notion, we establish $L^2$-estimates for holomorphic vector bundles with Nakano positive singular Hermitian metrics. We also show vanishing theorems, which generalize both Nakano type and Demailly-Nadel type vanishing theorems. As applications, we specifically construct globally Nakano semi-positive singular Hermitian metrics for several bundles, and prove vanishing theorems associated with them.

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BibTeXRIS

Takahiro Inayama. 2020-04-13. Nakano positivity of singular Hermitian metrics and vanishing theorems of Demailly-Nadel-Nakano type. https://doi.org/10.14231/ag-2022-003

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