Translator Disclaimer
15 March 2013 Flexible varieties and automorphism groups
I. Arzhantsev, H. Flenner, S. Kaliman, F. Kutzschebauch, M. Zaidenberg
Duke Math. J. 162(4): 767-823 (15 March 2013). DOI: 10.1215/00127094-2080132

Abstract

Given an irreducible affine algebraic variety X of dimension n2, 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 Xreg, then it is infinitely transitive on Xreg. In turn, the transitivity is equivalent to the flexibility of X. The latter means that for every smooth point xXreg the tangent space TxX is spanned by the velocity vectors at x of one-parameter unipotent subgroups of Aut(X). We also provide various modifications and applications.

Citation

Download Citation

I. Arzhantsev. H. Flenner. S. Kaliman. F. Kutzschebauch. M. Zaidenberg. "Flexible varieties and automorphism groups." Duke Math. J. 162 (4) 767 - 823, 15 March 2013. https://doi.org/10.1215/00127094-2080132

Information

Published: 15 March 2013
First available in Project Euclid: 15 March 2013

zbMATH: 1295.14057
MathSciNet: MR3039680
Digital Object Identifier: 10.1215/00127094-2080132

Subjects:
Primary: 14R20, 32M17
Secondary: 14L30

Rights: Copyright © 2013 Duke University Press

JOURNAL ARTICLE
57 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.162 • No. 4 • 15 March 2013
Back to Top