Equivariant degenerations of spherical modules for groups of type A

Details Equivariant degenerations of spherical modules for groups of type A Equivariant degenerations of spherical modules for groups of type A

2010-08-05

arxiv.org/abs/1008.0911v3

Mathematics

Algebraic Geometry

v3: 65 pages, minor corrections and changes to exposition following referee's suggestions, a shorter version will appear in An

Scientific paper

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.

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