Equivariant degenerations of spherical modules: part II

TL;DR

This paper extends the understanding of the moduli scheme of affine spherical G-varieties, showing it is an affine space for all reductive groups, not just type A, under certain conditions.

Contribution

It proves that the Alexeev-Brion moduli scheme M_S is an affine space for all reductive groups, removing previous restrictions on the group type.

Findings

M_S is an affine space for all reductive groups

The result generalizes previous work limited to type A groups

The paper confirms the structure of moduli schemes under broader conditions

Abstract

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.