Biswas, Indranil
(2009)
*On the finite principal bundles*
Annals of Global Analysis and Geometry, 35
(2).
pp. 181-190.
ISSN 0232-704X

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Official URL: http://www.springerlink.com/content/kt06785054qr10...

Related URL: http://dx.doi.org/10.1007/s10455-008-9129-5

## Abstract

Let G be a connected linear algebraic group defined over C. Fix a finite dimensional faithful G-module
V_{0}. A holomorphic principal G-bundle E _{G} over a compact connected Kahler manifold X is called finite if for each subquotient W of the G-module V_{0} , the holomorphic vector bundle E G (W) over X associated to E_{G} for W is finite. Given a holomorphic principal G-bundle E_{G} over X, we prove that the following four statements are equivalent: (1) The principal G-bundle E_{G} admits a flat holomorphic connection whose monodromy group is finite. (2) There is a finite etale Galois covering f : Y → X such that the pullback f*E_{G} is a holomorphically trivializable principal G-bundle over Y. (3) For any finite dimensional complex G-module W, the holomorphic vector bundle E_{G} (W) = E ×^{G}W over X, associated to the principal G-bundle E_{G} for the G-module W, is finite. (4) The principal G-bundle
E_{G} is finite.

Item Type: | Article |
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Source: | Copyright of this article belongs to Springer-Verlag. |

Keywords: | Principal Bundle; Finite Bundle; Kahler Manifold |

ID Code: | 3630 |

Deposited On: | 18 Oct 2010 10:17 |

Last Modified: | 27 Jan 2011 07:02 |

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