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

2012/12/18 by Hossein Raufi, Raufi, Hossein · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.AG #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.1212.4417

16 pages

arxiv created 2012/12/18 · openalex publication_date 2012/12/18 · arxiv updated 2012/12/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove the classical Nakano vanishing theorem with Hörmander L²-estimates on a compact Kähler manifold using Siu's so called ∂\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.

Citations

• Bergman kernels and the pseudoeffectivity of relative canonical bundles
• Singular hermitian metrics on holomorphic vector bundles

Cited by

• Asymptotic estimate of cohomology groups valued in pseudo-effective line bundles

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