Arzhantsev, I.; Flenner, H.; Kaliman, S.; Kutzschebauch, F.; Zaidenberg, M. (2013). Flexible varieties and automorphism groups. Duke Mathematical Journal, 162(4), pp. 767823. Duke University Press 10.1215/001270942080132

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Given an irreducible affine algebraic variety X of dimension n≥2 , we let SAut(X) denote the special automorphism group of X , that is, the subgroup of the full automorphism group Aut(X) generated by all oneparameter unipotent subgroups. We show that if SAut(X) is transitive on the smooth locus X reg , then it is infinitely transitive on X reg . In turn, the transitivity is equivalent to the flexibility of X . The latter means that for every smooth point x∈X reg the tangent space T x X is spanned by the velocity vectors at x of oneparameter unipotent subgroups of Aut(X) . We also provide various modifications and applications.
Item Type: 
Journal Article (Original Article) 

Division/Institute: 
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics 
UniBE Contributor: 
Kaliman, Shulim and Kutzschebauch, Frank 
Subjects: 
500 Science > 510 Mathematics 
ISSN: 
00127094 
Publisher: 
Duke University Press 
Language: 
English 
Submitter: 
Mario Amrein 
Date Deposited: 
12 Mar 2014 10:00 
Last Modified: 
07 Oct 2015 10:26 
Publisher DOI: 
10.1215/001270942080132 
BORIS DOI: 
10.7892/boris.41957 
URI: 
https://boris.unibe.ch/id/eprint/41957 