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Spherical orbit closures in simple projective spaces and their normalizations

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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/H ⊂ P(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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  1. Dipartimento di Matematica, “Guido Castelnuovo”, “Sapienza” Università di Roma, 00185, Roma, Italy

    J. Gandini

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  1. J. Gandini
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Gandini, J. Spherical orbit closures in simple projective spaces and their normalizations. Transformation Groups 16, 109–136 (2011). https://doi.org/10.1007/s00031-011-9120-2

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