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Etale triviality of finite vector bundles over compact complex manifolds
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- A vector bundle $E$ over a projective variety $M$ is called finite if it satisfies a nontrivial polynomial equation with nonnegative integral coefficients. Introducing finite bundles, Nori proved that $E$ is finite if and only if the pullback of $E$ to some finite \'etale covering of $M$ is trivializable \cite{No1}. The definition of finite bundles extends naturally to holomorphic vector bundles over compact complex manifolds. We prove that a holomorphic vector bundle over a compact complex manifold $M$ is finite if and only if the pullback of $E$ to some finite \'etale covering of $M$ is holomorphically trivializable. Therefore, $E$ is finite if and only if it admits a flat holomorphic connection with finite monodromy.<br />Comment: Final version
- Subjects :
- Mathematics - Differential Geometry
Connection (fibred manifold)
Pure mathematics
32L10, 53C55, 14D21
General Mathematics
Holomorphic function
Vector bundle
Pullback (differential geometry)
01 natural sciences
Mathematics - Algebraic Geometry
Mathematics::Algebraic Geometry
0103 physical sciences
FOS: Mathematics
0101 mathematics
Complex Variables (math.CV)
Mathematics::Symplectic Geometry
Algebraic Geometry (math.AG)
Holomorphic vector bundle
Projective variety
Mathematics
Mathematics - Complex Variables
Mathematics::Complex Variables
010102 general mathematics
Monodromy
Differential Geometry (math.DG)
010307 mathematical physics
Complex manifold
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....f62512905206bffbc5c2948cc0a6b71b
- Full Text :
- https://doi.org/10.48550/arxiv.2004.04089