A remark on Kov\'acs' vanishing theorem

TL;DR

This paper provides an alternative proof of Kovács' vanishing theorem using minimal model theory, avoiding the need for Du Bois pairs and reducing it to the relative Kawamata--Viehweg--Nadel vanishing theorem.

Contribution

It offers a new proof of Kovács' vanishing theorem based on standard minimal model theory techniques, simplifying the original approach.

Findings

Proof avoids Du Bois pairs

Reduces to Kawamata--Viehweg--Nadel vanishing

Simplifies understanding of Kovács' theorem

Abstract

We give an alternative proof of Kov\'acs' vanishing theorem. Our proof is based on the standard arguments of the minimal model theory. We do not need the notion of Du Bois pairs. We reduce Kov\'acs' vanishing theorem to the well-known relative Kawamata--Viehweg--Nadel vanishing theorem.