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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 spaces and toric varieties.
There is also a notion of real spherical varieties.
A projective spherical variety is a Mori dream space.
Spherical embeddings are classified by so-called colored fans, a generalization of fans for toric varieties; this is known as Luna-Vust Theory.
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