Singular principal bundles over higher dimensional manifolds and their moduli spaces

In 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 ${\varrho }^{\text{p}}\text{\hspace{0.17em}⁣}:G\text{lra}\text{SL}(V)$. 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.