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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 ...