Moduli of affine schemes with reductive group action

By Valery Alexeev, M. Brion. 2003

78 citations recorded by the source corpus.

For a connected reductive group G and a finite-dimensional G-module V, we study the invariant Hilbert scheme that parameterizes closed G-stable subschemes of V affording a fixed, multiplicity-finite representation of G in their coordinate ring. We construct an action on this invariant Hilbert scheme of a maximal torus T of G, together with an open T-stable subscheme admitting a good quotient. The fibers of the quotient map classify affine G-schemes having a prescribed categorical quotient by a maximal unipotent subgroup of G. We show that V contains only finitely many multiplicity-free G-subvarieties, up to the action of the centralizer of G in GL(V). As a consequence, there are only finitely many isomorphism classes of affine G-varieties affording a prescribed multiplicity-free representation in their coordinate ring. Final version, to appear in Journal of Algebraic Geometry

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d9aebaa8c025bb3b80558c90810391747d8c760b

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In Geometry and Topology

1. I. Losev
2. V. Ginzburg
3. T. Arakawa
4. A. Premet
5. I. Gordon
6. Ben Webster

In Mathematical Physics

1. I. Losev
2. V. Ginzburg
3. T. Arakawa
4. A. Premet
5. I. Gordon
6. Ben Webster

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