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

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.

arXiv comment43pages v1. 37pages v2: The condition in Theorem 1.6 and 6.1 was weakened, Corollary 6.2 was added, and the corresponding revisions were made