Spherical variety
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
References
- ↑ 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"
- Losev, Ivan (2006). "Proof of the Knop conjecture". arXiv:math/0612561.
- Losev, Ivan (2009). "Uniqueness properties for spherical varieties". arXiv:0904.2937.