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Local rigidity of quasi-regular varieties

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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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Authors and Affiliations

  1. Hausdorff Center for Mathematics, Universität Bonn, Villa Maria, Endenicher Allee 62, 53115, Bonn, Germany

    Boris Pasquier & Nicolas Perrin

  2. Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, Case 247, 4 place Jussieu, 75252, Paris Cedex 05, France

    Nicolas Perrin

Authors
  1. Boris Pasquier
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  2. Nicolas Perrin
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Correspondence to Boris Pasquier.

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Pasquier, B., Perrin, N. Local rigidity of quasi-regular varieties. Math. Z. 265, 589–600 (2010). https://doi.org/10.1007/s00209-009-0531-x

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  • DOI: https://doi.org/10.1007/s00209-009-0531-x

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