Unirationality and Existence of Infinitely Transitive Models

Fedor Bogomolov (), Ilya Karzhemanov () and Karine Kuyumzhiyan ()
Additional contact information
Fedor Bogomolov: New York University, Courant Institute of Mathematical Sciences
Ilya Karzhemanov: New York University, Courant Institute of Mathematical Sciences
Karine Kuyumzhiyan: National Research University Higher School of Economics

A chapter in Birational Geometry, Rational Curves, and Arithmetic, 2013, pp 77-92 from Springer

Abstract: 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.

Keywords: Open Subset; Complete Intersection; Algebraic Variety; Toric Variety; Ample Line Bundle (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-6482-2_4

Ordering information: This item can be ordered from
http://www.springer.com/9781461464822

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

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().