Stable spherical varieties and their moduli

Details Stable spherical varieties and their moduli Stable spherical varieties and their moduli

2005-05-31

arxiv.org/abs/math/0505673v1

Mathematics

Algebraic Geometry

50 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Stable spherical varieties and their moduli does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stable spherical varieties and their moduli, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stable spherical varieties and their moduli will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-455704