### Abstract

We study unirational algebraic varieties and the fields of rational functions on them. We show that after adding a finite number of variables some of these fields admit an infinitely transitive model. The latter is an algebraic variety with the given field of rational functions and an infinitely transitive regular action of a group of algebraic automorphisms generated by unipotent algebraic subgroups. We expect that this property holds for all unirational varieties and in fact is a peculiar one for this class of algebraic varieties among those varieties which are rationally connected.

Original language | English (US) |
---|---|

Title of host publication | Birational Geometry, Rational Curves, and Arithmetic |

Publisher | Springer New York |

Pages | 77-91 |

Number of pages | 15 |

ISBN (Electronic) | 9781461464822 |

ISBN (Print) | 9781461464815 |

DOIs | |

State | Published - Jan 1 2013 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Unirationality and existence of infinitely transitive models'. Together they form a unique fingerprint.

## Cite this

Bogomolov, F., Karzhemanov, I., & Kuyumzhiyan, K. (2013). Unirationality and existence of infinitely transitive models. In

*Birational Geometry, Rational Curves, and Arithmetic*(pp. 77-91). Springer New York. https://doi.org/10.1007/978-1-4614-6482-2_4