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The Nakano vanishing theorem and a vanishing theorem of Demailly-Nadel type for holomorphic vector bundles (1212.4417v1)
Published 18 Dec 2012 in math.CV, math.AG, and math.DG
Abstract: We prove the classical Nakano vanishing theorem with H\"ormander $L2$-estimates on a compact K\"ahler manifold using Siu's so called $\partial\dbar$-Bochner-Kodaira method, thereby avoiding the K\"ahler 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.