Flexible varieties and automorphism groups

I. Arzhantsev, H. Flenner, Shulim Kaliman, F. Kutzschebauch, M. Zaidenberg

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

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 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 x∈Xregthe 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.

Original languageEnglish (US)
Pages (from-to)767-823
Number of pages57
JournalDuke Mathematical Journal
Volume162
Issue number4
DOIs
StatePublished - Mar 1 2013

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Automorphism Group
Subgroup
Tangent Space
Transitivity
Algebraic Variety
Locus
Flexibility
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ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

Flexible varieties and automorphism groups. / Arzhantsev, I.; Flenner, H.; Kaliman, Shulim; Kutzschebauch, F.; Zaidenberg, M.

In: Duke Mathematical Journal, Vol. 162, No. 4, 01.03.2013, p. 767-823.

Research output: Contribution to journalArticle

Arzhantsev, I, Flenner, H, Kaliman, S, Kutzschebauch, F & Zaidenberg, M 2013, 'Flexible varieties and automorphism groups', Duke Mathematical Journal, vol. 162, no. 4, pp. 767-823. https://doi.org/10.1215/00127094-2080132
Arzhantsev I, Flenner H, Kaliman S, Kutzschebauch F, Zaidenberg M. Flexible varieties and automorphism groups. Duke Mathematical Journal. 2013 Mar 1;162(4):767-823. https://doi.org/10.1215/00127094-2080132
Arzhantsev, I. ; Flenner, H. ; Kaliman, Shulim ; Kutzschebauch, F. ; Zaidenberg, M. / Flexible varieties and automorphism groups. In: Duke Mathematical Journal. 2013 ; Vol. 162, No. 4. pp. 767-823.
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