A Compactification of the Universal Moduli Space of Principal G-Bundles

Let G be a semisimple linear algebraic group, ρ : G ↪ SL ( V ) a finite-dimensional faithful representation, g ≥ 2 a natural number, and δ a positive rational number. We prove the existence of a compactification of the universal moduli space of semistable principal G -bundles over M ¯ g , provided that δ is sufficiently large, having the following property: the fibers over singular curves are the moduli spaces of δ -semistable singular principal G -bundles.