Equivariant degenerations of spherical modules: part II

We determine, under a certain assumption, the Alexeev-Brion moduli scheme M_S of affine spherical G-varieties with a prescribed weight monoid S. In [ arXiv:1008.0911 ] we showed that if G is a connected complex reductive group of type A and S is the weight monoid of a spherical G-module, then M_S is an affine space. Here we prove that this remains true without any restriction on the type of G.