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Moduli of affine schemes with reductive group action | | Valery Alexeev
; Michel Brion
; | | Date: |
24 Dec 2002 | | Subject: | Algebraic Geometry; Representation Theory MSC-class: 14L30, 14D22, 14C05 | math.AG math.RT | | Abstract: | 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 | | Source: | arXiv, math.AG/0301288 | | Services: | Forum | Review | PDF | Favorites | |
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