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arXiv · 0807.2327

Local rigidity of quasi-regular varieties

Boris Pasquier·Nicolas Perrin
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Abstract

For a $G$-variety $X$ with an open orbit, we define its boundary $\partial X$ 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 $\partial X$. 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 F. Bien and M. Brion. We apply these results to study the local rigidity of the smooth projective varieties with Picard number one classified in a previous paper of the first author.

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Boris Pasquier, Nicolas Perrin. 2008-07-15. Local rigidity of quasi-regular varieties. https://arxiv.org/abs/0807.2327

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