Cohomologie des fibrés en droites sur la compactification magnifique d'un groupe semi-simple adjoint

Tchoudjem, Alexis

doi:10.1016/s1631-073x(02)02288-4

Cited by 4 publications

(2 citation statements)

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“…There are plenty of vector bundles with nontrivial infinitesimal deformations, but a direct sum of line bundles on the wonderful compactification has no nontrivial infinitesimal deformation (cf. Tchoudjem [31], [32], [33] and K [17]). However, there exists a line bundle with non-vanishing intermediate cohomologies in this case.…”

Section: Introductionmentioning

confidence: 99%

Equivariant vector bundles on group completions

Kato

2005

Journal für die reine und angewandte Mathematik (Crelles Journa

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In this paper, we describe the category of bi-equivariant vector bundles on a bi-equivariant smooth (partial) compactification of a reductive algebraic group with normal crossing boundary divisors. Our result is a generalization of the description of the category of equivariant vector bundles on toric varieties established by A.A. Klyachko [Math. USSR. Izvestiya, {\bf 35}, No.2 (1990)]. As an application, we prove splitting of equivariant vector bundles of low rank on the wonderful compactification of an adjoint semisimple group in the sense of C. De Concini and C. Procesi [Lecture Note in Math. {\bf 996} (1983)]. Moreover, we present an answer to a problem raised by B. Kostant in the case of complex groups.Comment: Final version. Improved Exposition. to appear in Crelle's J. 43page

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Section: Introductionmentioning

confidence: 99%

Equivariant vector bundles on group completions

Kato

2005

Journal für die reine und angewandte Mathematik (Crelles Journa

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“…In Proposition 2.4, we show that for all fixed point x of T in X, G.x is complete. This property seems to play a key role in several works about the embeddings of G × G/G (see for example, [Tch02]).…”

Section: Introductionmentioning

confidence: 98%

Spherical homogeneous spaces of minimal rank

Ressayre

2010

Advances in Mathematics

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Let $G$ be a complex connected reductive algebraic group and $G/B$ denote the flag variety of $G$. A $G$-homogeneous space $G/H$ is said to be {\it spherical} if $H$ acts on $G/B$ with finitely many orbits. A class of spherical homogeneous spaces containing the tori, the complete homogeneous spaces and the group $G$ (viewed as a $G\times G$-homogeneous space) has particularly nice proterties. Namely, the pair $(G,H)$ is called a {\it spherical pair of minimal rank} if there exists $x$ in $G/B$ such that the orbit $H.x$ of $x$ by $H$ is open in $G/B$ and the stabilizer $H_x$ of $x$ in $H$ contains a maximal torus of $H$. In this article, we study and classify the spherical pairs of minimal rank.Comment: Document produced in 200

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