The Kawamata--Viehweg--Nadel-type vanishing theorem and the asymptotic multiplier ideal sheaf

TL;DR

This paper proves new vanishing theorems related to asymptotic multiplier ideal sheaves on compact Kähler manifolds, extending classical results and providing a relative version.

Contribution

It establishes Nadel-type and Kawamata--Viehweg-type vanishing theorems for asymptotic multiplier ideal sheaves on compact Kähler manifolds, including a relative variant.

Findings

Proved Nadel-type vanishing theorem for asymptotic multiplier ideal sheaves.

Established Kawamata--Viehweg-type vanishing theorem in the same context.

Provided a relative version of the vanishing theorems.

Abstract

In this paper we establish a Nadel-type vanishing theorem and a Kawamata--Viehweg-type vanishing theorem concerning the asymptotic multiplier ideal sheaf on a compact K\"{a}hler manifold $X$. After that, we provide a relative variant.