Singular principal bundles on reducible nodal curves

Abstract

Studying degenerations of moduli spaces of semistable principal bundles on smooth curves leads to the problem of studying moduli spaces on singular curves. In this note, we will see that the moduli spaces of δ \delta -semistable pseudo bundles on a nodal curve become, for large values of δ \delta , the moduli spaces of semistable singular principal bundles. The latter are reasonable candidates for degenerations and a potential basis for further developments as on irreducible nodal curves. In particular, we find a notion of semistability for principal bundles on reducible nodal curves. The understanding of the asymptotic behavior of δ \delta -semistability rests on a lemma from geometric invariant theory. The results allow for the construction of a universal moduli space of semistable singular principal bundles over the moduli space of stable curves. Due to recent work of Wilson, this universal moduli space has a close relation to the sheaf of algebras of conformal blocks.