A generalization of Nadel vanishing theorem

TL;DR

This paper extends the Nadel vanishing theorem by proving a new $L^{2}$ existence theorem for line bundles with singular Hermitian metrics, broadening the scope of vanishing results in complex geometry.

Contribution

It introduces a generalized vanishing theorem based on an $L^{2}$ existence theorem for line bundles with singular Hermitian metrics, enhancing previous results.

Findings

Established a new $L^{2}$ existence theorem for singular Hermitian metrics.

Generalized the classical Nadel vanishing theorem.

Provided applications to complex algebraic geometry.

Abstract

In this paper we first prove a version of $L^{2}$ existence theorem for line bundles equipped a singular Hermitian metrics. Aa an application, we establish a vanishing theorem which generalizes the classical Nadel vanishing theorem.