Infinitely transitive actions on real affine suspensions

Details Infinitely transitive actions on real affine suspensions Infinitely transitive actions on real affine suspensions

2010-12-09

arxiv.org/abs/1012.1961v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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