Singular Principal Bundles on Algebraic Varieties
by
Alexander Schmitt
Universität Köln & Universität Duisburg-Essen

Singular principal bundles were used by the speaker to construct and compactify the moduli space of Ramanathan-stable principal G-bundles over a polarized projective manifold (X, O_X(1)) over the field of complex numbers, G being a semisimple linear algebraic group.

Meanwhile, these objects have been used also on singular varieties, esp.\ nodal curves (Bhosle/Schmitt), and on algebraic surfaces for obtaining an algebraic model for the Uhlenbeck compactification (Balaji). Other potential extensions concern positive characteristic and decorated principal bundles.

The speaker will give a survey of these topics.