Spherical orbit closures in simple projective spaces and their normalizations

Details Spherical orbit closures in simple projective spaces and their normalizations Spherical orbit closures in simple projective spaces and their normalizations

2009-07-07

arxiv.org/abs/0907.1177v4

Mathematics

Algebraic Geometry

24 pages, LaTeX. v4: Final version, to appear in Transformation Groups. Simplified some proofs and corrected minor mistakes, a

Scientific paper

Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module of finite dimension. If G/H \subset P(V) is a spherical orbit and if X is its closure, then we describe the orbits of X and those of its normalization. If moreover the wonderful completion of G/H is strict, then we give necessary and sufficient combinatorial conditions so that the normalization morphism is a homeomorphism. Such conditions are trivially fulfilled if G is simply laced or if H is a symmetric subgroup.

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