Holomorphic functions and vector bundles on coverings of projective varieties

Fedor Bogomolov, Bruno De Oliveira

Research output: Contribution to journalArticle

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 - Jan 1 2005

Fingerprint

Pullback
Projective Variety
Vector Bundle
Analytic function
Covering
Universal Cover
Imbedding
Isomorphism Classes

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Holomorphic functions and vector bundles on coverings of projective varieties. / Bogomolov, Fedor; De Oliveira, Bruno.

In: Asian Journal of Mathematics, Vol. 9, No. 3, 01.01.2005, p. 295-314.

Research output: Contribution to journalArticle

@article{84100957975640a1be68d7a27f7010b6,
title = "Holomorphic functions and vector bundles on coverings of projective varieties",
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.",
keywords = "Holomorphic functions, Projective varieties, Universal coverings, Vector bundles",
author = "Fedor Bogomolov and {De Oliveira}, Bruno",
year = "2005",
month = "1",
day = "1",
doi = "10.4310/AJM.2005.v9.n3.a1",
language = "English (US)",
volume = "9",
pages = "295--314",
journal = "Asian Journal of Mathematics",
issn = "1093-6106",
publisher = "International Press of Boston, Inc.",
number = "3",

}

TY - JOUR

T1 - Holomorphic functions and vector bundles on coverings of projective varieties

AU - Bogomolov, Fedor

AU - De Oliveira, Bruno

PY - 2005/1/1

Y1 - 2005/1/1

N2 - 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.

AB - 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.

KW - Holomorphic functions

KW - Projective varieties

KW - Universal coverings

KW - Vector bundles

UR - http://www.scopus.com/inward/record.url?scp=84872444492&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872444492&partnerID=8YFLogxK

U2 - 10.4310/AJM.2005.v9.n3.a1

DO - 10.4310/AJM.2005.v9.n3.a1

M3 - Article

VL - 9

SP - 295

EP - 314

JO - Asian Journal of Mathematics

JF - Asian Journal of Mathematics

SN - 1093-6106

IS - 3

ER -