Moduli of affine schemes with reductive group action
| dc.creator | Alexeev, Valery | |
| dc.creator | Brion, Michel | |
| dc.date | 2003-01-24 | |
| dc.date | 2003-09-15 | |
| dc.date.accessioned | 2026-07-07T04:54:40Z | |
| dc.date.available | 2026-07-07T04:54:40Z | |
| dc.description | 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 | |
| dc.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/math/0301288 | |
| dc.identifier | http://arxiv.org/abs/math/0301288 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66348 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 14L30, 14D22, 14C05 | |
| dc.title | Moduli of affine schemes with reductive group action | |
| dc.type | text |