Uniqueness property for spherical homogeneous spaces
By I. Losev. 2007
96 citations recorded by the source corpus.
Let G be a connected reductive group. Recall that a homogeneous G-space X is called spherical if a Borel subgroup B ⊂ G has an open orbit on X. To X one assigns certain combinatorial invariants: the weight lattice, the valuation cone and the set of B-stable prime divisors. We prove that two spherical homogeneous spaces with the same combinatorial invariants are equivariantly isomorphic. Further, we recover the group of G-equivariant automorphisms of X from these invariants.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/38f5de9425a369f5d5f250a6c873f31d195beaa3
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The Spherical Systems of the Wonderful Reductive Subgroups (2011, unknown): “The classification of all the spherical subgroups of a reductive group is a consequence of the Luna conjecture whose proof has been completed recently with the contribution of several authors, see [13, 15, 5, 2, 12, 4, 3, 6, 7] (and also [9] for a different approach).”
- Primitive wonderful varieties (2011, background): “It is known that these invariants distinguish between different G-isomorphism classes of wonderful varieties (see [10]), therefore the classification is achieved if one proves that each primitive system is geometrically realizable, i.”
- K-stability of Fano spherical varieties (2016, background): “us, while the former is not toroidal. 3.1.3. Equivariant automorphisms. The classification of spherical embeddings up to G-equivariant automorphisms, together with the deep uniqueness Theorem of Losev [Los09], shows that the neutral component of the group of G-equivariant automorphisms of a spherical”