## Asian Journal of Mathematics

### Holomorphic Functions and Vector Bundles on Coverings of Projective Varieties

#### 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