Moduli spaces of principal bundles on singular varieties

TL;DR

This paper proves the existence of a projective relative moduli space for semistable singular principal bundles over fibers of a flat, projective morphism, extending previous results from nodal curves to more general singular varieties.

Contribution

It generalizes the construction of moduli spaces of semistable principal bundles from nodal curves to broader classes of singular varieties.

Findings

Existence of a projective relative moduli space for semistable singular principal bundles.

Extension of Schmitt's results from nodal curves to more general singular fibers.

Framework applicable to a wide class of singular algebraic varieties.

Abstract

Let k be an algebraically closed field of characteristic zero. Let f:X-->S be a flat, projective morphism of k-schemes of finite type with integral geometric fibers. We prove existence of a projective relative moduli space for semistable singular principal bundles on the fibres of f. This generalizes the result of A. Schmitt who studied the case when X is a nodal curve.