Holomorphic Functions of Exponential Growth on Abelian Coverings of a Projective Manifold

2000/01/14 by Alexander Brudnyi, Brudnyi, Alexander
Mathematics · #14E20 #32A17 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:14E20 #msc:32A17

paper · pdf · doi:10.48550/arxiv.math/0001088

arxiv created 2000/01/14 · openalex publication_date 2000/01/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a projective manifold, p:M_G --> M a regular covering over M with a free abelian transformation group G. We describe holomorphic functions on M_G of an exponential growth with respect to the distance defined by a metric pulled back from M. As a corollary we obtain for such functions Cartwright and Liouville type theorems. Our approach brings together L₂ cohomology technique for holomorphic vector bundles on complete Kähler manifolds and geometric properties of projective manifolds.

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