Unirationality and existence of infinitely transitive models

Fedor Bogomolov; Ilya Karzhemanov; Karine Kuyumzhiyan

doi:10.1007/978-1-4614-6482-2_4

Unirationality and existence of infinitely transitive models

Fedor Bogomolov, Ilya Karzhemanov, Karine Kuyumzhiyan

Mathematics

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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	https://doi.org/10.1007/978-1-4614-6482-2_4
State	Published - Jan 1 2013

ASJC Scopus subject areas

General Mathematics

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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.

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ER -

Unirationality and existence of infinitely transitive models

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