Local rigidity of quasi-regular varieties

Boris Pasquier; Nicolas Perrin

doi:10.1007/s00209-009-0531-x

Local rigidity of quasi-regular varieties

Boris Pasquier
, Nicolas Perrin

University Bonn
Université Paris Cité

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

For a G-variety X with an open orbit, we define its boundary ∂ X as the complement of the open orbit. The action sheaf S_X is the subsheaf of the tangent sheaf made of vector fields tangent to ∂ X. We prove, for a large family of smooth spherical varieties, the vanishing of the cohomology groups Hⁱ(X, S_X) for i > 0, extending results of Bien and Brion (Compos. Math. 104:1-26, 1996). We apply these results to study the local rigidity of the smooth projective varieties with Picard number one classified in Pasquier (Math. Ann., in press).

langue originale	Anglais
Pages (de - à)	589-600
Nombre de pages	12
journal	Mathematische Zeitschrift
Volume	265
Numéro de publication	3
Les DOIs	https://doi.org/10.1007/s00209-009-0531-x
état	Publié - 1 juil. 2010
Modification externe	Oui

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10.1007/s00209-009-0531-x

Contient cette citation

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abstract = "For a G-variety X with an open orbit, we define its boundary ∂ X as the complement of the open orbit. The action sheaf SX is the subsheaf of the tangent sheaf made of vector fields tangent to ∂ X. We prove, for a large family of smooth spherical varieties, the vanishing of the cohomology groups Hi(X, SX) for i > 0, extending results of Bien and Brion (Compos. Math. 104:1-26, 1996). We apply these results to study the local rigidity of the smooth projective varieties with Picard number one classified in Pasquier (Math. Ann., in press).",

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Local rigidity of quasi-regular varieties

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