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Unirationality and Existence of Infinitely Transitive Models

In: Birational Geometry, Rational Curves, and Arithmetic

Author

Listed:
  • Fedor Bogomolov

    (New York University, Courant Institute of Mathematical Sciences
    National Research University Higher School of Economics)

  • Ilya Karzhemanov

    (New York University, Courant Institute of Mathematical Sciences)

  • Karine Kuyumzhiyan

    (National Research University Higher School of Economics)

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.

Suggested Citation

  • Fedor Bogomolov & Ilya Karzhemanov & Karine Kuyumzhiyan, 2013. "Unirationality and Existence of Infinitely Transitive Models," Springer Books, in: Fedor Bogomolov & Brendan Hassett & Yuri Tschinkel (ed.), Birational Geometry, Rational Curves, and Arithmetic, edition 127, pages 77-92, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-6482-2_4
    DOI: 10.1007/978-1-4614-6482-2_4
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