Bogomolov-Sommese type vanishing theorem for holomorphic vector bundles equipped with positive singular Hermitian metrics

TL;DR

This paper generalizes the Bogomolov-Sommese vanishing theorem to holomorphic vector bundles with positive singular Hermitian metrics, using L2-estimates and multiplier ideal sheaves.

Contribution

It introduces a dual Nakano semi-positivity condition for singular Hermitian metrics and proves a new vanishing theorem extending previous results.

Findings

Established a vanishing theorem for big line bundles with multiplier ideal sheaves.

Defined dual Nakano semi-positivity for singular Hermitian metrics.

Generalized the Bogomolov-Sommese vanishing theorem to holomorphic vector bundles.

Abstract

We obtain the Bogomolov-Sommese type vanishing theorem involving multiplier ideal sheaves for big line bundles. We define a dual Nakano semi-positivity of singular Hermitian metrics with L2-estimates and prove the vanishing theorem which is a generalization of the Bogomolov-Sommese type vanishing theorem to holomorphic vector bundles.