User:KonradVoelkel/Spherical Variety

A spherical variety is an algebraic variety X together with an algebraic group operation by a reductive linear algebraic group G such that there exists an open orbit of the Borel subgroup of G.

Some ideas for an article:
 * there exists a geometric classification of spherical varieties over the complex numbers. --> Luna
 * spherical diagrams (any better name?)
 * special case: smooth projective spherical varieties. What is known here?
 * special case: reductive group G is split over the ground field of X. What is known now?
 * special case: toric varieties (which notions of toric varieties carry over?)
 * wonderful compactification
 * the motive of a spherical variety is Tate. --> which "kind" of motive? where is it proved?
 * literature references ...