Holomorphic functions and vector bundles on coverings of projective varieties

Fedor Bogomolov; Bruno De Oliveira

doi:10.4310/AJM.2005.v9.n3.a1

Holomorphic functions and vector bundles on coverings of projective varieties

Fedor Bogomolov, Bruno De Oliveira

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	295-314
Number of pages	20
Journal	Asian Journal of Mathematics
Volume	9
Issue number	3
DOIs	https://doi.org/10.4310/AJM.2005.v9.n3.a1
State	Published - 2005

Keywords

Holomorphic functions
Projective varieties
Universal coverings
Vector bundles

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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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",

note = "Funding Information: ∗Received September 22, 2004; accepted for publication March 7, 2005. †Courant Institute for Mathematical Sciences, New York University, New York, N.Y. 10003-6668, USA (bogomolo@cims.nyu.edu). The author is partially supported by NSF grant DMS-0100837. ‡Department of Mathematics, University of Miami, Coral Gables, FL 33124, USA (bdeolive @math.miami.edu). The author is partially supported by NSF Postoctoral Research Fellowship DMS-9902393 and NSF grant DMS-0306487.",

year = "2005",

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.",

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

AU - Bogomolov, Fedor

AU - De Oliveira, Bruno

N1 - Funding Information: ∗Received September 22, 2004; accepted for publication March 7, 2005. †Courant Institute for Mathematical Sciences, New York University, New York, N.Y. 10003-6668, USA (bogomolo@cims.nyu.edu). The author is partially supported by NSF grant DMS-0100837. ‡Department of Mathematics, University of Miami, Coral Gables, FL 33124, USA (bdeolive @math.miami.edu). The author is partially supported by NSF Postoctoral Research Fellowship DMS-9902393 and NSF grant DMS-0306487.

PY - 2005

Y1 - 2005

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

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