Geometric characterization of excellent affine spherical homogeneous spaces

Details Geometric characterization of excellent affine spherical homogeneous spaces Geometric characterization of excellent affine spherical homogeneous spaces

2011-06-28

arxiv.org/abs/1106.5677v1

Mathematics

Algebraic Geometry

16 pages

Scientific paper

A spherical homogeneous space of a connected semisimple algebraic group G is said to be excellent if it is quasi-affine and its weight semigroup is generated by disjoint linear combinations of fundamental weights of G. We prove that, for an affine spherical homogeneous space G/H, the condition of being excellent is equivalent to the following two conditions holding simultaneously: first, the factorization morphism G/H \to Y = Spec {}^U C[G/H] for the action on G/H of a maximal unipotent subgroup U of G is equidimensional; second, Y \simeq C^r for some r.

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