Asian Journal of Mathematics

Holomorphic Functions and Vector Bundles on Coverings of Projective Varieties

Fedor Bogomolov and Bruno De Oliveira

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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.

Article information

Source
Asian J. Math., Volume 9, Number 3 (2005), 295-314.

Dates
First available in Project Euclid: 3 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1146673622

Mathematical Reviews number (MathSciNet)
MR2214954

Zentralblatt MATH identifier
1122.14033

Citation

Bogomolov, Fedor; De Oliveira, Bruno. Holomorphic Functions and Vector Bundles on Coverings of Projective Varieties. Asian J. Math. 9 (2005), no. 3, 295--314. https://projecteuclid.org/euclid.ajm/1146673622


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