Seminar Algebra and Geometry: Ronan Terpereau (Universität Mainz)

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 θ, we explain how to construct the moduli space M of θ-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 θ-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 μ: M → X//G which turns to be a “nice” desingularization of the quotient X//G in many situations.

Export event as iCal