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Moduli spaces of (G,h)-constellations

Tanja Becker 1
1 Topologie, géométrie et algèbre
LMJL - Laboratoire de Mathématiques Jean Leray
Abstract : Given a reductive group G acting on an affine scheme X over C and a Hilbert function h: Irr G → N_0, we construct the moduli space M_θ(X) of θ-stable (G,h)-constellations on X, which is a common generalisation of the invariant Hilbert scheme after Alexeev and Brion and the moduli space of θ-stable G-constellations for finite groups G introduced by Craw and Ishii. Our construction of a morphism M_θ(X) → X//G makes this moduli space a candidate for a resolution of singularities of the quotient X//G. Furthermore, we determine the invariant Hilbert scheme of the zero fibre of the moment map of an action of Sl_2 on (C²)⁶ as one of the first examples of invariant Hilbert schemes with multiplicities. While doing this, we present a general procedure for the realisation of such calculations. We also consider questions of smoothness and connectedness and thereby show that our Hilbert scheme gives a resolution of singularities of the symplectic reduction of the action.
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https://tel.archives-ouvertes.fr/tel-00675853
Contributor : Tanja Becker <>
Submitted on : Friday, March 2, 2012 - 10:09:58 AM
Last modification on : Monday, March 25, 2019 - 4:52:06 PM
Long-term archiving on: : Friday, November 23, 2012 - 3:30:46 PM

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  • HAL Id : tel-00675853, version 1

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Tanja Becker. Moduli spaces of (G,h)-constellations. Algebraic Geometry [math.AG]. Université de Nantes, 2011. English. ⟨tel-00675853⟩

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