Nodal Uniformization of G-bundles

Abstract

We give a survey of uniformization results for principal bundles on curves. We provide a proof of uniformization for nodal curves; this result is a special case of work of Belkale and Fakhruddin for uniformization on singular curves. We use the uniformization result to give a construction of a compactification of the moduli of G bundles on a family of nodal curves. Along the way we also explain how to use equivariant compactifactions of a group to compactify the moduli stack of bundles over a fixed nodal curve.

arXiv comment8 pages, reworked section 3 to address misstatement and fix an error, also made simplification in proof of prop 4.4