Flexible varieties and automorphism groups

I. Arzhantsev; H. Flenner; S. Kaliman; F. Kutzschebauch; M. Zaidenberg

doi:10.1215/00127094-2080132

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arXiv · 1011.5375

Flexible varieties and automorphism groups

I. Arzhantsev·H. Flenner·S. Kaliman·F. Kutzschebauch·M. Zaidenberg

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Abstract

Given an affine algebraic variety X of dimension at least 2, we let SAut (X) denote the special automorphism group of X i.e., 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 of X then it is infinitely transitive on this locus. In turn, the transitivity is equivalent to the flexibility of X. The latter means that for every smooth point x of X the tangent space at x is spanned by the velocity vectors of one-parameter unipotent subgroups of Aut (X). We provide also different variations and applications.

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BibTeX RIS

I. Arzhantsev, H. Flenner, S. Kaliman, F. Kutzschebauch, M. Zaidenberg. 2010-11-24. Flexible varieties and automorphism groups. https://doi.org/10.1215/00127094-2080132

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