A Le Potier-type isomorphism twisted with multiplier submodule sheaves

TL;DR

This paper establishes a Le Potier-type isomorphism involving multiplier submodule sheaves, leading to new vanishing and injectivity theorems for holomorphic vector bundles with singular Hermitian metrics.

Contribution

It introduces a novel Le Potier-type isomorphism twisted with multiplier submodule sheaves, extending classical results to singular Hermitian metrics.

Findings

Proves a Kollár-type injectivity theorem.

Derives a Nadel-type vanishing theorem.

Establishes a singular holomorphic Morse inequality.

Abstract

In this paper, we obtain a Le Potier-type isomorphism theorem twisted with multiplier submodule sheaves, which relates a holomorphic vector bundle endowed with a strongly Nakano semipositive singular Hermitian metric to the tautological line bundle with the induced metric. As applications, we obtain a Koll\'ar-type injectivity theorem, a Nadel-type vanishing theorem, and a singular holomorphic Morse inequality for holomorphic vector bundles and so on.