Infinitely transitive actions on real affine suspensions
Algebraic Geometry
2013-05-29 v2
Abstract
A group G acts infinitely transitively on a set Y if for every positive integer m, its action is m-transitive on Y. Given a real affine algebraic variety Y of dimension greater than or equal to two, we show that, under a mild restriction, if the special automorphism group of Y (the group generated by one-parameter unipotent subgroups) is infinitely transitive on each connected component of the smooth locus of Y, then for any real affine suspension X over Y, the special automorphism group of X is infinitely transitive on each connected component of the smooth locus of X. This generalizes a recent result by Arzhantsev, Kuyumzhiyan and Zaidenberg over the field of real numbers.
Cite
@article{arxiv.1012.1961,
title = {Infinitely transitive actions on real affine suspensions},
author = {Karine Kuyumzhiyan and Frédéric Mangolte},
journal= {arXiv preprint arXiv:1012.1961},
year = {2013}
}