Unirationality and existence of infinitely transitive models

Fedor Bogomolov, Ilya Karzhemanov, Karine Kuyumzhiyan

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish (US)
Title of host publicationBirational Geometry, Rational Curves, and Arithmetic
PublisherSpringer New York
Pages77-91
Number of pages15
ISBN (Electronic)9781461464822
ISBN (Print)9781461464815
DOIs
StatePublished - Jan 1 2013

ASJC Scopus subject areas

  • Mathematics(all)

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  • 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