Kodaira-type Vanishings via Non-abelian Hodge Theory

TL;DR

This paper employs non-abelian Hodge theory to extend classical vanishing theorems, including Saito and Kawamata-Viehweg types, to broader contexts involving mixed twistor D-modules and Q-divisors.

Contribution

It introduces new generalizations of Kodaira vanishing theorems using non-abelian Hodge theory and mixed twistor D-modules, extending their applicability.

Findings

Generalized Saito vanishing with mixed twistor D-modules

Extended vanishing to Q-divisors with Kawamata-Viehweg type

Proved a relative vanishing theorem for projective morphisms

Abstract

In this paper, we use non-abelian Hodge Theory to study Kodaira type vanishings and its generalizations. In particular, we generalize Saito vanishing using Mixed Twistor D-modules. We also generalize it to a Kawamata-Viehweg type vanishing using Q-divisors, and we also prove a relative version for a projective morphism.