Paolo Bravi (2010)
Les cours du CIRM
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We give a short introduction to the problem of classification of spherical varieties, by presenting the Luna conjecture about the classification of wonderful varieties and illustrating some of the related currently known results.
Guido Pezzini (2010)
Les cours du CIRM
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These notes contain an introduction to the theory of spherical and wonderful varieties. We describe the Luna-Vust theory of embeddings of spherical homogeneous spaces, and explain how wonderful varieties fit in the theory.
Dmitri Akhiezer (2009)
Annales de l’institut Fourier
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We consider an action of a connected compact Lie group on a Stein manifold by holomorphic transformations. We prove that the manifold is spherical if and only if there exists an antiholomorphic involution preserving each orbit. Moreover, for a spherical Stein manifold, we construct an antiholomorphic involution, which is equivariant with respect to the Weyl involution of the acting group, and show that this involution stabilizes each orbit. The construction uses some properties of spherical...
Giovanna Carnovale (2009)
Annales de l’institut Fourier
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Let be a connected, reductive algebraic group over an algebraically closed field of zero or good and odd characteristic. We characterize spherical conjugacy classes in as those intersecting only Bruhat cells in corresponding to involutions in the Weyl group of .
Ivan V. Losev (2009)
Annales de l’institut Fourier
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In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoid are equivariantly isomorphic. We also state and prove a uniqueness property for (not necessarily smooth) affine spherical varieties.