Nakano-Nadel type, Bogomolov-Sommese type vanishing and singular dual Nakano semi-positivity

TL;DR

This paper explores properties of singular Nakano semi-positivity and establishes vanishing theorems involving $L^2$-methods on weakly pseudoconvex manifolds, with applications to Fujita's conjecture.

Contribution

It introduces new vanishing theorems for singular (dual) Nakano semi-positivity using $L^2$-techniques and applies these results to problems related to Fujita's conjecture.

Findings

Established singular vanishing theorems using $L^2$-estimates.

Proved properties of singular (dual) Nakano semi-positivity.

Applied results to Fujita's conjecture with singular metrics.

Abstract

In this article, we get properties for singular (dual) Nakano semi-positivity and obtain singular type vanishing theorem involving $L^2$-subsheaves on weakly pseudoconvex manifolds by $L^2$-estimates and $L^2$-type Dolbeault isomorphisms. As applications, Fujita's conjecture type theorem with singular Hermitian metrics is presented.