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Mat. Sb., 2017, Volume 208, Number 2, Pages 121–148 (Mi msb8625)  

Flexibility of affine horospherical varieties of semisimple groups

A. A. Shafarevich

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University

Abstract: Let $k$ be an algebraically closed field of characteristic zero and $\mathbb{G}_a=(k,+)$ the additive group of $k$. An algebraic variety $X$ is said to be flexible if the tangent space at every regular point of $X$ is generated by the tangent vectors to orbits of various regular actions of $\mathbb{G}_a$. In 1972, Vinberg and Popov introduced the class of affine $S$-varieties which are also known as affine horospherical varieties. These are varieties on which a connected algebraic group acts with an open orbit in such a way that the stationary subgroup of each point in the orbit contains a maximal unipotent subgroup of $G$. In this paper the flexibility of affine horospherical varieties of semisimple groups is proved.
Bibliography: 9 titles.

Keywords: algebraic groups, affine horospherical varieties, flexibility.

DOI: https://doi.org/10.4213/sm8625

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English version:
Sbornik: Mathematics, 2017, 208:2, 285–310

Bibliographic databases:

UDC: 512.745
MSC: Primary 14R20; Secondary 32M05
Received: 23.10.2015 and 28.08.2016

Citation: A. A. Shafarevich, “Flexibility of affine horospherical varieties of semisimple groups”, Mat. Sb., 208:2 (2017), 121–148; Sb. Math., 208:2 (2017), 285–310

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