2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63084In this note, we introduce the notion of a singular principal G-bundle, associated to a reductive algebraic group G over the complex numbers by means of a faithful representation $\varrho^\p\colon G\lra \SL(V)$. This concept is meant to provide an analogon to the notion of a torsion free sheaf as a generalization of the notion of a vector bundle. We will construct moduli spaces for these singular principal bundles which compactify the moduli spaces of stable principal bundles.To appear in the International Mathematics Research Notices (IMRN), 20 pagesAlgebraic Geometrytext