2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71272We substantially refine the theory of singular principal bundles introduced in a former paper. In particular, we show that we need only honest singular principal bundles in our compactification. These are objects which carry the structure of a rational principal bundle in the sense of Ramanathan. Moreover, we arrive at a much simpler semistability condition. In the case of a semisimple group, this is just the Gieseker-version of Ramanathan's semistability condition for the corresponding rational principal $G$-bundle.To appear in the International Mathematics Research Notices. V2: Minor correctionsAlgebraic Geometrytext