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

Publisher | Springer New York |

Pages | 77-91 |

Number of pages | 15 |

ISBN (Print) | 9781461464822, 9781461464815 |

DOIs | |

State | Published - Jan 1 2013 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

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

**Unirationality and existence of infinitely transitive models.** / Bogomolov, Fedor; Karzhemanov, Ilya; Kuyumzhiyan, Karine.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

T1 - Unirationality and existence of infinitely transitive models

AU - Bogomolov, Fedor

AU - Karzhemanov, Ilya

AU - Kuyumzhiyan, Karine

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84901974946&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84901974946&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-6482-2_4

DO - 10.1007/978-1-4614-6482-2_4

M3 - Chapter

AN - SCOPUS:84901974946

SN - 9781461464822

SN - 9781461464815

SP - 77

EP - 91

BT - Birational Geometry, Rational Curves, and Arithmetic

PB - Springer New York

ER -