Results 1 - 10 of 29

Wonderful varieties of type C

by Paolo Bravi, Guido Pezzini , 2003
"... Abstract. Let G be a connected semisimple group over C, whose simple components have type A or D. We prove that wonderful G-varieties are classified by means of combinatorial objects called spherical systems. This is a generalization of a known result of Luna for groups of type A; thanks to another ..."
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Abstract. Let G be a connected semisimple group over C, whose simple components have type A or D. We prove that wonderful G-varieties are classified by means of combinatorial objects called spherical systems. This is a generalization of a known result of Luna for groups of type A; thanks to another result of Luna, this implies also the classification of all spherical G-varieties for the groups G we are considering. For these G we also prove the smoothness of the embedding of Demazure. 1.
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An introduction to wonderful varieties with many examples of type F4

by P. Bravi, D. Luna , 2008
"... ..."
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PROOF OF THE KNOP CONJECTURE

by Ivan V. Losev , 2007
"... Abstract. In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoids are equivariantly isomorphic. Contents ..."
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Abstract. In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoids are equivariantly isomorphic. Contents
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Classification of strict wonderful varieties

by P. Bravi, S. Cupit-foutou - arXiv:0806.2263v1 . P. BRAVI AND G. PEZZINI
"... Abstract. In the setting of strict wonderful varieties we answer positively to Luna’s conjecture, saying that wonderful varieties are classified by combinatorial objects, the so-called spherical systems. In particular, we prove that strict wonderful varieties are mostly obtained from symmetric space ..."
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Abstract. In the setting of strict wonderful varieties we answer positively to Luna’s conjecture, saying that wonderful varieties are classified by combinatorial objects, the so-called spherical systems. In particular, we prove that strict wonderful varieties are mostly obtained from symmetric spaces, spherical nilpotent orbits or model spaces. To make the paper self-contained as much as possible, we shall gather some known results on these families and
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Wonderful varieties: a geometrical realization

by S. Cupit-foutou
"... Abstract. We give a geometrical realization of wonderful varieties by means of a suitable class of invariant Hilbert schemes. Consequently, we prove Luna’s conjecture asserting that wonderful varieties can be classified by some triples of combinatorial invariants: the spherical systems. ..."
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Abstract. We give a geometrical realization of wonderful varieties by means of a suitable class of invariant Hilbert schemes. Consequently, we prove Luna’s conjecture asserting that wonderful varieties can be classified by some triples of combinatorial invariants: the spherical systems.
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INVARIANT HILBERT SCHEMES AND WONDERFUL VARIETIES

by Stéphanie Cupit-Foutou , 2008
"... The invariant Hilbert schemes considered in [4] were proved to be affine spaces. The proof relied on the classification of strict wonderful varieties. We obtain in the present article a classification-free proof of the affinity of these invariant Hilbert scheme by means of deformation theoretical ar ..."
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The invariant Hilbert schemes considered in [4] were proved to be affine spaces. The proof relied on the classification of strict wonderful varieties. We obtain in the present article a classification-free proof of the affinity of these invariant Hilbert scheme by means of deformation theoretical arguments. As a consequence we recover in a shorter way the classification of strict wonderful varieties. This provides an alternative and new approach to answer Luna’s conjecture.

Primitive spherical systems

by P. Bravi , 909
"... A spherical system is a combinatorial object, arising in the theory of wonderful varieties, defined in terms of a root system. All spherical systems can be obtained by means of some general combinatorial procedures (parabolic induction, fiber product and projective fibration) from the socalled primi ..."
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A spherical system is a combinatorial object, arising in the theory of wonderful varieties, defined in terms of a root system. All spherical systems can be obtained by means of some general combinatorial procedures (parabolic induction, fiber product and projective fibration) from the socalled primitive spherical systems. Here we report the list of all primitive spherical systems.

AUTOMORPHISMS OF WONDERFUL VARIETIES

by Guido Pezzini , 802
"... Abstract. Let G be a complex semisimple linear algebraic group, and X a wonderful G-variety. We determine the connected automorphism group Aut 0 (X) and we calculate Luna’s invariants of X under its action. 1. ..."
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Abstract. Let G be a complex semisimple linear algebraic group, and X a wonderful G-variety. We determine the connected automorphism group Aut 0 (X) and we calculate Luna’s invariants of X under its action. 1.
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A constructive approach to the classification of wonderful varieties

by P. Bravi, G. Pezzini
"... ar ..."
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COMPUTATION OF WEYL GROUPS OF G-VARIETIES

by Ivan V. Losev
"... Abstract. Let G be a connected reductive group. To any irreducible G-variety one assigns a certain linear group generated by reflections called the Weyl group. Weyl groups play an important role in the study of embeddings of homogeneous spaces. We establish algorithms for computing Weyl groups for h ..."
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Abstract. Let G be a connected reductive group. To any irreducible G-variety one assigns a certain linear group generated by reflections called the Weyl group. Weyl groups play an important role in the study of embeddings of homogeneous spaces. We establish algorithms for computing Weyl groups for homogeneous spaces and affine homogeneous vector bundles. For some special classes of G-varieties (affine homogeneous vector bundles of maximal rank, affine homogeneous spaces, homogeneous spaces of maximal rank with a discrete group of central automorphisms) we compute Weyl groups more or less explicitly. Contents
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