Holomorphic functions and vector bundles on coverings of projective varieties

Fedor Bogomolov, Bruno De Oliveira

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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

Original languageEnglish (US)
Pages (from-to)295-314
Number of pages20
JournalAsian Journal of Mathematics
Volume9
Issue number3
DOIs
StatePublished - 2005

Keywords

  • Holomorphic functions
  • Projective varieties
  • Universal coverings
  • Vector bundles

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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