Duke Mathematical Journal
- Duke Math. J.
- Volume 162, Number 4 (2013), 767-823.
Flexible varieties and automorphism groups
Given an irreducible affine algebraic variety of dimension , we let denote the special automorphism group of , that is, the subgroup of the full automorphism group generated by all one-parameter unipotent subgroups. We show that if is transitive on the smooth locus , then it is infinitely transitive on . In turn, the transitivity is equivalent to the flexibility of . The latter means that for every smooth point the tangent space is spanned by the velocity vectors at of one-parameter unipotent subgroups of . We also provide various modifications and applications.
Duke Math. J., Volume 162, Number 4 (2013), 767-823.
First available in Project Euclid: 15 March 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14R20: Group actions on affine varieties [See also 13A50, 14L30] 32M17: Automorphism groups of Cn and affine manifolds
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
Arzhantsev, I.; Flenner, H.; Kaliman, S.; Kutzschebauch, F.; Zaidenberg, M. Flexible varieties and automorphism groups. Duke Math. J. 162 (2013), no. 4, 767--823. doi:10.1215/00127094-2080132. https://projecteuclid.org/euclid.dmj/1363355693