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In algebraic geometry, given a reductive algebraic group G and a Borel subgroup B, a spherical variety is a G-variety with an open dense B-orbit. It is sometimes also assumed to be normal. Examples are flag varieties, symmetric space and (affine or projective) toric varieties.

A projective spherical variety is a Mori dream space.[1]

Losev (2006) has shown that every "smooth" affine spherical variety is uniquely determined by its weight monoid. (see Brion for the definition of weight monoid.)
See also

Luna–Vust theory


Brion, Michel (2007). "The total coordinate ring of a wonderful variety". Journal of Algebra 313 (1): 61–99. doi:10.1016/j.jalgebra.2006.12.022.

Michel Brion, "Introduction to actions of algebraic groups" [1]
Losev, Ivan (2006). "Proof of the Knop conjecture". arXiv:math/0612561.
Losev, Ivan (2009). "Uniqueness properties for spherical varieties". arXiv:0904.2937.

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