Principal G-bundles on nodal curves

Bhosle, Usha N. (2001) Principal G-bundles on nodal curves Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 111 (3). pp. 271-291. ISSN 0253-4142

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Let G be a connected semisimple affine algebraic group defined over C. We study the relation between stable, semistable G-bundles on a nodal curve Y and representations of the fundamental group of Y. This study is done by extending the notion of (generalized) parabolic vector bundles to principal G-bundles on the desingularization C of Y and using the correspondence between them and principal G-bundles on Y. We give an isomorphism of the stack of generalized parabolic bundles on C with a quotient stack associated to loop groups. We show that if G is simple and simply connected then the Picard group of the stack of principal G-bundles on Y is isomorphic to ⊕mZ, m being the number of components of Y.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Principal Bundles; Loop Groups; Parabolic Bundles
ID Code:3415
Deposited On:11 Oct 2010 09:02
Last Modified:16 May 2016 14:13

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