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29
Wonderful varieties of type C
, 2003
"... Abstract. Let G be a connected semisimple group over C, whose simple components have type A or D. We prove that wonderful Gvarieties 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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Cited by 20 (7 self)
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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 Gvarieties 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 Gvarieties for the groups G we are considering. For these G we also prove the smoothness of the embedding of Demazure. 1.
PROOF OF THE KNOP CONJECTURE
, 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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Cited by 15 (3 self)
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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
Classification of strict wonderful varieties
 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 socalled spherical systems. In particular, we prove that strict wonderful varieties are mostly obtained from symmetric space ..."
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Cited by 11 (8 self)
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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 socalled 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 selfcontained as much as possible, we shall gather some known results on these families and
Wonderful varieties: a geometrical realization
"... 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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Cited by 9 (0 self)
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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.
INVARIANT HILBERT SCHEMES AND WONDERFUL VARIETIES
, 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 classificationfree proof of the affinity of these invariant Hilbert scheme by means of deformation theoretical ar ..."
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Cited by 9 (1 self)
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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 classificationfree 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
, 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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Cited by 7 (5 self)
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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
, 802
"... Abstract. Let G be a complex semisimple linear algebraic group, and X a wonderful Gvariety. 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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Cited by 7 (3 self)
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Abstract. Let G be a complex semisimple linear algebraic group, and X a wonderful Gvariety. We determine the connected automorphism group Aut 0 (X) and we calculate Luna’s invariants of X under its action. 1.
COMPUTATION OF WEYL GROUPS OF GVARIETIES
"... Abstract. Let G be a connected reductive group. To any irreducible Gvariety 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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Cited by 5 (5 self)
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Abstract. Let G be a connected reductive group. To any irreducible Gvariety 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 Gvarieties (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