Transformation Groups

, Volume 16, Issue 1, pp 109–136 | Cite as

Spherical orbit closures in simple projective spaces and their normalizations

Article

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. If G/HP(V) is a spherical orbit and if \( X = \overline {G/H} \) is its closure, then we describe the orbits of X and those of its normalization \( \tilde{X} \) . If, moreover, the wonderful completion of G/H is strict, then we give necessary and sufficient combinatorial conditions so that the normalization morphism \( \tilde{X} \to X \) is a homeomorphism. Such conditions are trivially fulfilled if G is simply laced or if H is a symmetric subgroup.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Dipartimento di Matematica, “Guido Castelnuovo”“Sapienza” Università di RomaRomaItaly

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