Flexibility of affine horospherical varieties of semisimple groups
Sbornik. Mathematics, Tome 208 (2017) no. 2, pp. 285-310
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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.
@article{SM_2017_208_2_a6,
author = {A. A. Shafarevich},
title = {Flexibility of affine horospherical varieties of semisimple groups},
journal = {Sbornik. Mathematics},
pages = {285--310},
publisher = {mathdoc},
volume = {208},
number = {2},
year = {2017},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2017_208_2_a6/}
}
A. A. Shafarevich. Flexibility of affine horospherical varieties of semisimple groups. Sbornik. Mathematics, Tome 208 (2017) no. 2, pp. 285-310. http://geodesic.mathdoc.fr/item/SM_2017_208_2_a6/