Flexible varieties and automorphism groups

Arzhantsev, I.; Flenner, H.; Kaliman, S.; Kutzschebauch, F.; Zaidenberg, M. (2013). Flexible varieties and automorphism groups. Duke Mathematical Journal, 162(4), pp. 767-823. Duke University Press 10.1215/00127094-2080132

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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 one-parameter 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 one-parameter 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:

0012-7094

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:

10.1215/00127094-2080132

BORIS DOI:

10.7892/boris.41957

URI:

https://boris.unibe.ch/id/eprint/41957

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