@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",

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. Funding Information: The author is partially supported by NSF Postoctoral Research Fellowship DMS-9902393 and NSF grant DMS-0306487. Publisher Copyright: {\textcopyright} 2005 International Press.",

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.",

number = "3",

}