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

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.

29pages; final version + a minor remark

References in corpus (1)

• Positivity of holomorphic vector bundles in terms of $L^p$-conditions of $\bar{\partial }$

Cited by in corpus (1)

• Dual Nakano positivity and singular Nakano positivity of direct image sheaves