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 language | English (US) |
|---|---|
| Pages (from-to) | 767-823 |
| Number of pages | 57 |
| Journal | Duke Mathematical Journal |
| Volume | 162 |
| Issue number | 4 |
| DOIs | |
| State | Published - Mar 1 2013 |
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ASJC Scopus subject areas
- Mathematics(all)
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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 journal › Article
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TY - JOUR
T1 - Flexible varieties and automorphism groups
AU - Arzhantsev, I.
AU - Flenner, H.
AU - Kaliman, Shulim
AU - Kutzschebauch, F.
AU - Zaidenberg, M.
PY - 2013/3/1
Y1 - 2013/3/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84877146397&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84877146397&partnerID=8YFLogxK
U2 - 10.1215/00127094-2080132
DO - 10.1215/00127094-2080132
M3 - Article
AN - SCOPUS:84877146397
VL - 162
SP - 767
EP - 823
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
SN - 0012-7094
IS - 4
ER -