Principal G-bundles on nodal curves

Abstract

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.