On the cohomology groups of holomorphic Banach bundles

2008/10/30 by László Lempert, Laszlo Lempert, Lempert, Laszlo
Mathematics · #32L05 #32L10 #58B15 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32L05 #msc:32L10 #msc:58B15

paper · pdf · doi:10.48550/arxiv.0810.5429

14 pages

arxiv created 2008/10/30 · openalex publication_date 2008/10/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a compact complex manifold M, and introduce the notion of two holomorphic Banach bundles E,F over M being compact perturbations of one another. Given two such bundles we show that if the cohomology groups H^q(M,E) are finite dimensional then so are the cohomology groups H^q(M,F); as well as a more precise result in the same spirit.

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