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

Research output: Contribution to journal › Article › peer-review

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 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).

Original language	English
Pages (from-to)	589-600
Number of pages	12
Journal	Mathematische Zeitschrift
Volume	265
Issue number	3
DOIs	https://doi.org/10.1007/s00209-009-0531-x
Publication status	Published - 1 Jul 2010
Externally published	Yes

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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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AB - 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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DO - 10.1007/s00209-009-0531-x

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JO - Mathematische Zeitschrift

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Local rigidity of quasi-regular varieties

Abstract

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