Poincar\'e families of G-bundles on a curve

TL;DR

This paper investigates the existence of Poincaré bundles over moduli spaces of stable principal G-bundles on algebraic curves, providing comprehensive conditions and obstruction class computations for all reductive groups and characteristics.

Contribution

It generalizes previous results by establishing necessary and sufficient conditions for Poincaré bundle existence across all reductive groups, topological types, and characteristics.

Findings

Derived conditions for Poincaré bundle existence

Computed orders of obstruction classes

Extended results to all reductive groups and characteristics

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 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.