Moduli spaces of principal bundles on singular varieties

Abstract

Let $k$ be an algebraically closed field of characteristic zero. Let $f:X\to S$ be a flat, projective morphism of $k$-schemes of finite type with integral geometric fibers. We prove the existence of a projective relative moduli space for semistable singular principal bundles on the fibers of $f$.

This generalizes the result of A. Schmitt, who studied the case when $X$ is a nodal curve.