Local rigidity of quasi-regular varieties |
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Authors: | Boris Pasquier Nicolas Perrin |
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Institution: | 1. Hausdorff Center for Mathematics, Universit?t Bonn, Villa Maria, Endenicher Allee 62, 53115, Bonn, Germany 2. Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, Case 247, 4 place Jussieu, 75252, Paris Cedex 05, France
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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 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 H
i
(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). |
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Keywords: | |
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