Kodaira-type Vanishings via Non-abelian Hodge Theory

Abstract

In this paper, we use nonabelian Hodge theory to study Kodaira-type vanishings. In particular, we generalize Saito vanishing using mixed twistor $\sD$-modules. We also generalize it to a Kawamata-Viehweg type vanishing using $\Q$-divisors, and prove an effective global generation theorem, as an application. We also prove a relative vanishing for a projective morphism in the mixed twistor $\sD$-module setting.

arXiv commentKMS admissibility gaps are fixed; 33 pages, accepted by JPAA