On the finite principal bundles

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


Let G be a connected linear algebraic group defined over C. Fix a finite dimensional faithful G-module V0. 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 V0 , the holomorphic vector bundle E G (W) over X associated to EG for W is finite. Given a holomorphic principal G-bundle EG over X, we prove that the following four statements are equivalent: (1) The principal G-bundle EG 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*EG is a holomorphically trivializable principal G-bundle over Y. (3) For any finite dimensional complex G-module W, the holomorphic vector bundle EG (W) = E ×GW over X, associated to the principal G-bundle EG for the G-module W, is finite. (4) The principal G-bundle EG is finite.

Item Type:Article
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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