Vanishing and semipositivity theorems for semi-log canonical pairs

Abstract

We prove an effective vanishing theorem for direct images of log pluricanonical bundles of projective semi-log canonical pairs. As an application, we obtain a semipositivity theorem for direct images of relative log pluricanonical bundles of projective semi-log canonical pairs over curves, which implies the projectivity of the moduli spaces of stable varieties. It is worth mentioning that we do not use the theory of variation of (mixed) Hodge structure.

13 pages, v2: very minor revisions, v3: references and address were updated, v4: minor revisions, references were updated

References in corpus (3)

• On semipositivity, injectivity and vanishing theorems
• Projectivity of the moduli space of stable log-varieties and subadditvity of log-Kodaira dimension
• A vanishing theorem of Koll'ar-Ohsawa type

Cited by in corpus (3)

• Injectivity theorem for pseudo-effective line bundles and its applications
• On semipositivity, injectivity and vanishing theorems
• Some Kollar-Enoki type injectivity and Nadel type vanishing theorems on compact Kahler manifolds