Equivariant Chow Ring and Chern Classes of Wonderful Symmetric Varieties of Minimal Rank

Brion, Michel; Joshua, Roy

doi:10.1007/s00031-008-9020-2

Cited by 21 publications

(18 citation statements)

References 18 publications

(30 reference statements)

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“…The minimal rank symmetric spaces were introduced by Brion [1]. Brion and Joshua have studied the geometry of the closures in X of the B-orbits in G/H, whenever G/H is of minimal rank [2]. Tchoudjem has also studied the closures in X of the B-orbits in G/H, whenever G/H is of minimal rank [19].…”

Section: Introductionmentioning

confidence: 99%

Equivariant vector bundles on complete symmetric varieties of minimal rank

2014

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Let X be the wonderful compactification of a complex symmetric space G/H of minimal rank. For a point x ∈ G, denote by Z the closure of BxH/H in X, where B is a Borel subgroup of G. The universal cover of G is denoted by [Formula: see text]. Given a [Formula: see text] equivariant vector bundle E on X, we prove that E is nef (respectively, ample) if and only if its restriction to Z is nef (respectively, ample). Similarly, E is trivial if and only if its restriction to Z is so.

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Section: Introductionmentioning

confidence: 99%

Equivariant vector bundles on complete symmetric varieties of minimal rank

2014

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“…We have not been able to describe its cohomology, partly because the number of classes is too big. In principle one should be able to deduce it from the cohomology of its blowup along the closed orbit, which should be accessible using [7,9,19]. What we have been able to check is that DG is infinitesimally rigid, a question motivated by a longstanding interest for the rigidity properties of homogeneous and quasi-homogeneous spaces (see for example [11,4,12]).…”

Section: Introductionmentioning

confidence: 99%

The Cayley Grassmannian

Manivel

2018

Journal of Algebra

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We study the smooth projective symmetric variety of Picard number one that compactifies the exceptional complex Lie group G 2 , by describing it in terms of vector bundles on the spinor variety of Spin 14 . We call it the double Cayley Grassmannian because quite remarkably, it exhibits very similar properties to those of the Cayley Grassmannian (the other symmetric variety of type G 2 ), but doubled in the certain sense. We deduce among other things that all smooth projective symmetric varieties of Picard number one are infinitesimally rigid.

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“…14,3.1,THEOREM]; it is known as the wonderful compactification. The wonderful compactification of G will be denoted by G. Fix a maximal torus T of G, and denote by T the closure of the variety T in the wonderful compactification G [BJ,§ 1]. Let Aut(T ) denote the group of all holomorphic automorphisms of T .…”

Section: Introductionmentioning

confidence: 99%

The full automorphism group ofT‾

Biswas

Kannan

Nagaraj

2017

Comptes Rendus. Mathématique

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Let G be the wonderful compactification of a simple affine algebraic group G of adjoint type defined over C. Let T ⊂ G be the closure of a maximal torus T ⊂ G. We prove that the group of all automorphisms of the variety T is the semi-direct product N G (T ) ⋊ D, where N G (T ) is the normalizer of T in G and D is the group of all automorphisms of the Dynkin diagram, if G = PSL(2, C). Note that if G = PSL(2, C), then T = CP 1 and so in this case Aut(T ) = PSL(2, C).Résumé. Le groupe complet des automorphismes de T . Soit G la compactification magnifique d'un groupe algébrique affine simple G de type adjoint défini sur C. Soit T ⊂ G la clôture d'un tore maximal T ⊂ G. Si G = PSL(2, C), nous montrons que le groupe de tous les automorphismes de la variété T est le produit semi-direct N G (T ) ⋊ D, où N G (T ) est le normalisateur de T dans G et D est le groupe de tous les automorphismes du diagramme de Dynkin. Remarquez que si G = PSL(2, C), alors T = CP 1 et donc dans ce cas Aut(T ) = PSL(2, C).

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Equivariant Chow Ring and Chern Classes of Wonderful Symmetric Varieties of Minimal Rank

Cited by 21 publications

References 18 publications

Equivariant vector bundles on complete symmetric varieties of minimal rank

Equivariant vector bundles on complete symmetric varieties of minimal rank

The Cayley Grassmannian

The full automorphism group ofT‾

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