Uniqueness property for spherical homogeneous spaces
代数几何
2009-05-30 v4 表示论
摘要
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.
引用
@article{arxiv.math/0703543,
title = {Uniqueness property for spherical homogeneous spaces},
author = {Ivan V. Losev},
journal= {arXiv preprint arXiv:math/0703543},
year = {2009}
}
备注
v1 25 pages, v2 22 pages, some proofs modified, some notation changed, final section removed, v3 minor modifications made v4 final version, to apper in Duke Math J