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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
Department of Mathematics, Ben Gurion University of the Negev, PO Box 653, Beer-Sheva 84105, Israel. E-mail:
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Let M be a projective manifold, p: MGM 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.

Research Article
© 2001 Kluwer Academic Publishers