2013/05/28 by Hubert Flenner, Shulim Kaliman, Flenner, Hubert +3 · 2 citations
Computer Science · Mathematics · #14R20 #32M17 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1305.6417
openalex publication_date 2013/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An affine variety X of dimension ≥ 2 is called \em flexible if its special automorphism group SAut(X) acts transitively on the smooth locus Xreg \citeAKZ. Recall that the special automorphism group SAut(X) is the subgroup of the automorphism group Aut(X) generated by all one-parameter unipotent subgroups \citeAKZ. Given a normal, flexible, affine variety X and a closed subvariety Y in X of codimension at least 2, we show that the pointwise stabilizer subgroup of Y in the group SAut(X) acts infinitely transitively on the complement X\backslash Y, that is, m-transitively for any m≥ 1. More generally we show such a result for any quasi-affine variety X and codimension ≥ 2 subset Y of X. In the particular case of X=Ån, n≥ 2, this yields a Theorem of Gromov and Winkelmann \citeGr1, \citeWi.