Séminaire de Mathématique
# Moduli of Parabolic Bundles, Quiver Representations, and the additive Deligne-Simpson problem

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Amphitéâtre Léon Motchane (IHES)
### Amphitéâtre Léon Motchane

#### IHES

Le Bois Marie
35, route de Chartres
91440 Bures-sur-Yvette

Description

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.

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