Holomorphic functions of polynomial growth on abelian coverings of a compact complex manifold
type: Item
instance of: scholarly article
title: Holomorphic functions of polynomial growth on abelian coverings of a compact complex manifold
zbMATH Open document ID: 0914.58002
author: Alexander Brudnyi
published in: Communications in Analysis and Geometry
publication date: 1999-06-06T00:00:00Z
review text: Let \(M\) be a compact complex manifold and \(p:M_G\to M\) be a regular covering over \(M\) with a free abelian transformation group \(G\). The author proves that under some assumptions on \(G\) the space \({\mathcal P}_l(M_G)\) of holomorphic functions on \(M_G\) of \(l\)-polynomial growth is finite dimensional and is linearly imbedded into the corresponding space \({\mathcal P}_l(\mathbb C^N)\) of holomorphic polynomials on \(\mathbb C^N\) with \(N=\frac 12 \text{ rank}(G)\).
Mathematics Subject Classification ID: 58C10
Mathematics Subject Classification ID: 58D15
zbMATH DE Number: 1223305
zbMATH Keywords: polynomial growth
zbMATH Keywords: free abelian transformation group
zbMATH Keywords: holomorphic function
zbMATH Keywords: holomorphic polynomial
reviewed by: Witold Mozgawa
MaRDI profile type: Publication
DOI: 10.4310/CAG.1998.V6.N3.A3
description: scientific article; zbMATH DE number 1223305