Uniqueness property for spherical homogeneous spaces

Details Uniqueness property for spherical homogeneous spaces Uniqueness property for spherical homogeneous spaces

2007-03-19

arxiv.org/abs/math/0703543v4

Duke Math. J. 147(2009), n.2., 315-343

Mathematics

Algebraic Geometry

v1 25 pages, v2 22 pages, some proofs modified, some notation changed, final section removed, v3 minor modifications made v4 f

Scientific paper

Let G be a connected reductive group. Recall that a G-variety X is called spherical if X is normal and a Borel subgroup of G has an open orbit on X. To a spherical homogeneous G-space 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 show how to recover the group of G-equivariant automorphisms from these invariants.

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