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

Published online by Cambridge University Press:  04 December 2007

Alexander Brudnyi
Alexander Brudnyi
Affiliation:
Department of Mathematics, Ben Gurion University of the Negev, PO Box 653, Beer-Sheva 84105, Israel. E-mail: brudnyi@cs.bgu.ac.il
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Abstract

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

Keywords

holomorphic functionL2 cohomologyregular covering with an Abelian transformation grouppositive vector bundle
Type
Research Article
Information
Compositio Mathematica , Volume 127 , Issue 1 , May 2001 , pp. 69 - 81
Copyright
© 2001 Kluwer Academic Publishers