Classification of smooth affine spherical varieties

Abstract

Let G be a complex reductive group. A normal G-variety X is called spherical if a Borel subgroup of G has a dense orbit in X. Of particular interest are spherical varieties which are smooth and affine since they form local models for multiplicity free Hamiltonian K-manifolds, K a maximal compact subgroup of G. In this paper, we classify all smooth affine spherical varieties up to coverings, central tori, and C*-fibrations.

v1: 23 pages, uses texdraw; v2: 25 pages, introduction updated, Lemma 7.2 fixed, references added, typos corrected