Chennai Mathematical Institute


3:30 pm, Lecture Hall 6
Torsors on semistable curves and the problem of degenerations

V Balaji
Chennai Mathematical Institute.


We answer two long-standing questions in the classification of $G$-torsors on curves for a simple, simply connected algebraic group $G$ over the field of complex numbers. The first question is to give an intrinsic definition of (semi)stability for a $G$-torsor on an {\em irreducible nodal curve} and the second one is the construction of a flat degeneration of the moduli space of semistable $G$-torsors when the smooth curve degenerates to an irreducible nodal curve. A generalization of the classical Bruhat-Tits group schemes to two-dimensional regular local rings and an application of the geometric formulation of the McKay correspondence provide the key tools.

This is the second talk in a two-talk series.