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September 2005 Holomorphic Functions and Vector Bundles on Coverings of Projective Varieties
Fedor Bogomolov, Bruno De Oliveira
Asian J. Math. 9(3): 295-314 (September 2005).

Abstract

Let $X$ be a projective manifold, $\rho:\tilde X \to X$ its universal covering and $\rho^*: Vect (X) \to Vect(\tilde X)$ the pullback map for the isomorphism classes of vector bundles. This article establishes a connection between the properties of the pullback map $\rho^*$ and the properties of the function theory on $\tilde X$. We prove the following pivotal result: if a universal cover of a projective variety has no nonconstant holomorphic functions then the pullback map $\rho^*$ is almost an imbedding.

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Fedor Bogomolov. Bruno De Oliveira. "Holomorphic Functions and Vector Bundles on Coverings of Projective Varieties." Asian J. Math. 9 (3) 295 - 314, September 2005.

Information

Published: September 2005
First available in Project Euclid: 3 May 2006

zbMATH: 1122.14033
MathSciNet: MR2214954

Rights: Copyright © 2005 International Press of Boston

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Vol.9 • No. 3 • September 2005
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