Local rigidity of quasi-regular varieties

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
14 pages

Keywords

Algebraic Geometry, 14L30; 14M17; 14B12; 14F10

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/164943

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0807.2327
 http://arxiv.org/abs/0807.2327

Collections

arXiv