Equivariant degenerations of spherical modules for groups of type A

Abstract

Let G be a complex reductive algebraic group. Fix a Borel subgroup B of G, with unipotent radical U, and a maximal torus T in B with character group X(T). Let S be a submonoid of X(T) generated by finitely many dominant weights. V. Alexeev and M. Brion introduced a moduli scheme M_S which classifies pairs (X,f) where X is an affine G-variety and f is a T-equivariant isomorphism between the categorical quotient of X by U and the toric variety determined by S. In this paper, we prove that M_S is isomorphic to an affine space when S is the weight monoid of a spherical G-module with G of type A.

v3: 65 pages, minor corrections and changes to exposition following referee's suggestions, a shorter version will appear in Annales de l'Institut Fourier

References in corpus (5)

• Wonderful Varieties: A geometrical realization
• Automorphisms of multiplicity free Hamiltonian manifolds
• An introduction to wonderful varieties with many examples of type F4
• Equivariant degenerations of spherical modules for groups of type A
• Invariant Hilbert schemes and Wonderful varieties

Cited by in corpus (5)

• New and old results on spherical varieties via moduli theory
• On the irreducible components of moduli schemes for affine spherical varieties
• The moduli scheme of affine spherical varieties with a free weight monoid
• Equivariant degenerations of spherical modules for groups of type A
• Invariant deformation theory of affine schemes with reductive group action