Algebraic Geometry Seminar

We study the singularities of the Drinfeld-Lafforgue-Vinberg

compactification of the moduli stack of G-bundles on a smooth projective curve for a reductive

group G. The definition of this compactification is due to Drinfeld and relies on the

Vinberg semigroup of G. We will mostly focus on the case G=SL_2; in this case the

compactification can alternatively be viewed as a canonical one-parameter

degeneration of the moduli stack of SL_2-bundles. We then study the

singularities of this one-parameter degeneration via the associated nearby cycles

construction. Time permitting, we might sketch a generalization to the case of an arbitrary

reductive group G and the relation to Langlands duality.