Holomorphic Functions of Exponential Growth on Abelian Coverings of a Projective Manifold
Complex Variables
2007-05-23 v1
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 L_{2} cohomology technique for holomorphic vector bundles on complete K\"{a}hler manifolds and geometric properties of projective manifolds.
Keywords
Cite
@article{arxiv.math/0001088,
title = {Holomorphic Functions of Exponential Growth on Abelian Coverings of a Projective Manifold},
author = {Alexander Brudnyi},
journal= {arXiv preprint arXiv:math/0001088},
year = {2007}
}