An example of an Sl₂-Hilbert scheme with multiplicities

2010/10/18 by Tanja Becker, Becker, Tanja
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1010.3622

Abstract

We determine the invariant Hilbert scheme of the zero fibre of the moment map of an action of Sl₂ on (C²)⁶ as one of the first examples of invariant Hilbert schemes with multiplicities. While doing this, we present a general procedure how to realise the calculation of invariant Hilbert schemes, which have been introduced by Alexeev and Brion. 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.

Citations

• Algebraic Families on an Algebraic Surface

Related

• SL₂-action on Hilbert schemes and Calogero-Moser spaces
• Schémas de Hilbert invariants et théorie classique des invariants
• Invariant Hilbert schemes
• Partial resolutions of Hilbert type, Dynkin diagrams, and generalized Kummer varieties
• Invariant Hilbert scheme resolution of Popov's SL(2)-varieties II: the non-toric case