On a characterization of finite vector bundles as vector bundles admitting a flat connection with finite monodromy group
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- by Indranil Biswas, Yogish I. Holla and Georg Schumacher PDF
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Abstract:
We prove that a holomorphic vector bundle $E$ over a compact connected Kähler manifold admits a flat connection, with a finite group as its monodromy, if and only if there are two distinct polynomials $f$ and $g$, with nonnegative integral coefficients, such that the vector bundle $f(E)$ is isomorphic to $g(E)$. An analogous result is proved for vector bundles over connected smooth quasi-projective varieties, of arbitrary dimension, admitting a flat connection with finite monodromy group. When the base space is a connected projective variety, or a connected smooth quasi-projective curve, the above characterization of vector bundles admitting a flat connection with finite monodromy group was established by M. V. Nori.References
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Additional Information
- Indranil Biswas
- Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
- MR Author ID: 340073
- Email: indranil@math.tifr.res.in
- Yogish I. Holla
- Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
- Email: yogi@math.tifr.res.in
- Georg Schumacher
- Affiliation: Fachbereich Mathematik der Philipps-Universität, Hans-Meerwein-Strasse, Lahn- berge, D-35032 Marburg, Germany
- MR Author ID: 193042
- ORCID: 0000-0003-3514-2415
- Email: schumac@mathematik.uni-marburg.de
- Received by editor(s): May 5, 1998
- Received by editor(s) in revised form: March 1, 1999
- Published electronically: June 21, 2000
- Communicated by: Ronald A. Fintushel
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3661-3669
- MSC (1991): Primary 53C07, 14F05
- DOI: https://doi.org/10.1090/S0002-9939-00-05478-2
- MathSciNet review: 1695096