Stable spherical varieties and their moduli

dc.creatorAlexeev, Valery
dc.creatorBrion, Michel
dc.date2005-05-31
dc.date.accessioned2026-07-07T05:20:24Z
dc.date.available2026-07-07T05:20:24Z
dc.descriptionWe 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.description50 pages
dc.identifierhttps://arxiv.org/abs/math/0505673
dc.identifierhttp://arxiv.org/abs/math/0505673
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75364
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subject14D20, 14L30, 14M17, 14M25, 20G05
dc.titleStable spherical varieties and their moduli
dc.typetext

Files

Collections