Spherical orbit closures in simple projective spaces and their normalizations

Abstract

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.

24 pages, LaTeX. v4: Final version, to appear in Transformation Groups. Simplified some proofs and corrected minor mistakes, added references. v3: major changes due to a mistake in previous versions

Cited by in corpus (6)

• Orbits of strongly solvable spherical subgroups on the flag variety
• Projective normality of model varieties and related results
• Regular functions on spherical nilpotent orbits in complex symmetric pairs: classical non-Hermitian cases
• (Quasi-)Hamiltonian manifolds of cohomogeneity one
• Degenerations of spherical subalgebras and spherical roots
• Momentum polytopes of projective spherical varieties and related Kähler geometry