The Nakano vanishing theorem and a vanishing theorem of Demailly-Nadel type for holomorphic vector bundles

Abstract

We prove the classical Nakano vanishing theorem with Hörmander $L^2$-estimates on a compact Kähler manifold using Siu's so called $\partial\dbar$-Bochner-Kodaira method, thereby avoiding the Kähler identities completely. We then introduce singular hermitian metrics on holomorphic vector bundles, and proceed to prove a vanishing theorem of Demailly-Nadel type for these in the special case where the base manifold is a Riemann surface.

16 pages

Cited by in corpus (2)

• Asymptotic estimate of cohomology groups valued in pseudo-effective line bundles
• An extension theorem of Ohsawa-Takegoshi type for sections of a vector bundle