Stable spherical varieties and their moduli
| dc.creator | Alexeev, Valery | |
| dc.creator | Brion, Michel | |
| dc.date | 2005-05-31 | |
| dc.date.accessioned | 2026-07-07T05:20:24Z | |
| dc.date.available | 2026-07-07T05:20:24Z | |
| dc.description | We introduce a notion of stable spherical variety which includes the spherical varieties under a reductive group $G$ and their flat equivariant degenerations. Given any projective space $\bP$ where $G$ acts linearly, we construct a moduli space for stable spherical varieties over $\bP$, that is, pairs $(X,f)$, where $X$ is a stable spherical variety and $f : X \to \bP$ is a finite equivariant morphism. This space is projective, and its irreducible components are rational. It generalizes the moduli space of pairs $(X,D)$, where $X$ is a stable toric variety and $D$ is an effective ample Cartier divisor on $X$ which contains no orbit. The equivariant automorphism group of $\bP$ acts on our moduli space; the spherical varieties over $\bP$ and their stable limits form only finitely many orbits. A variant of this moduli space gives another view to the compactifications of quotients of thin Schubert cells constructed by Kapranov and Lafforgue. | |
| dc.description | 50 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505673 | |
| dc.identifier | http://arxiv.org/abs/math/0505673 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75364 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 14D20, 14L30, 14M17, 14M25, 20G05 | |
| dc.title | Stable spherical varieties and their moduli | |
| dc.type | text |