Séminaire de Mathématique

Moduli of Parabolic Bundles, Quiver Representations, and the additive Deligne-Simpson problem

by Prof. Alexander SOIBELMAN (University of North Carolina)

Amphitéâtre Léon Motchane (IHES)

Amphitéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
The "very good" property for algebraic stacks was introduced by Beilinson and Drinfeld in their paper "The Quantization of Hitchin's Integrable System and Hecke Eigensheaves". They proved that for a semisimple complex group G, the moduli stack of G-bundles over a smooth complex projective curve X is "very good" as long as X has genus g > 1. We will introduce the "very good" property in the context of a group action on an algebraic variety, and prove it for a moduli space of parabolic bundles on P1 arising from quiver representations. As a special case, we will consider the "very good" property for the diagonal action of the group PGL(n) on a product of partial flag varieties and its relationship with the space of solutions to the additive Deligne-Simpson problem.