Poincaré families of G-bundles on a curve

Details Poincaré families of G-bundles on a curve Poincaré families of G-bundles on a curve

2010-01-13

arxiv.org/abs/1001.2123v2

Mathematics

Algebraic Geometry

18 pages. v2: minor changes. final version, to appear in Math. Annalen

Scientific paper

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 previous results of Newstead, Ramanan and Balaji-Biswas-Nagaraj-Newstead to all reductive groups, to all topological types of bundles, and also to all characteristics.

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