# Abstract des Vortrages von Ronan Terpereau

Moduli spaces of (G,h)-constellations

This talk focuses on a work initiated by Tanja Becker in her PhD thesis three years ago and completed recently by myself.

Given a reductive group G acting on an affine scheme X, a Hilbert function h, and a stability condition \theta, we explain how to construct the moduli space M of \theta-stable (G,h)-constellations on X, which is a common generalization of the invariant Hilbert scheme after Alexeev and Brion and of the moduli space of \theta-stable G-constellations for finite groups introduced by Craw and Ishii. The main tools for this construction are the geometric invariant theory and the invariant Quot schemes. Moreover, the moduli space M is naturally equipped with a morphism \mu: M \to X//G which turns to be a “nice” desingularization of the quotient X//G in many situations.