User:KonradVoelkel/Spherical Variety

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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 ...