### 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 X_{reg}, then it is infinitely transitive on X_{reg}. In turn, the transitivity is equivalent to the flexibility of X. The latter means that for every smooth point x∈X_{reg}the tangent space T_{x}X 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 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Flexible varieties and automorphism groups'. Together they form a unique fingerprint.

## Cite this

*Duke Mathematical Journal*,

*162*(4), 767-823. https://doi.org/10.1215/00127094-2080132