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 | |
| State | Published - 2005 |
Keywords
- Holomorphic functions
- Projective varieties
- Universal coverings
- Vector bundles
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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Bogomolov, F., & De Oliveira, B. (2005). Holomorphic functions and vector bundles on coverings of projective varieties. Asian Journal of Mathematics, 9(3), 295-314. https://doi.org/10.4310/AJM.2005.v9.n3.a1