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

2022/02/14 by Yuta Watanabe, Watanabe, Yuta
Mathematics · #14F17 #14F18 #32L10 #32L20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2202.06603

openalex publication_date 2022/02/14 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

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.

Related

• Nadel-Nakano vanishing theorems of vector bundles with singular Hermitian metrics
• Singular hermitian metrics on vector bundles
• Positivity of Singular Hermitian Metrics for Holomorphic Vector Bundles
• The Nakano vanishing theorem and a vanishing theorem of Demailly-Nadel type for holomorphic vector bundles
• Multiplier Submodule Sheaves and a problem of Lempert