Poincaré families of G-bundles on a curve (Pre-published version)

Abstract

Let G be a reductive group over an algebraically closed field k. Consider the moduli space of stable principal G-bundles on a smooth projective curve C over k. We give necessary and sufficient conditions for the existence of Poincar´e bundles over open subsets of this moduli space, and compute the orders of the corresponding obstruction classes. This generalizes the previ-ous results of Newstead, Ramanan and Balaji-Biswas-Nagaraj-Newstead to all reductive groups, to all topological types of bundles, and also to all character-istics.