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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Codimension two integral points on some rationally connected threefolds are potentially dense

Authors: David McKinnon and Mike Roth
Journal: J. Algebraic Geom. 31 (2022), 345-386
Published electronically: December 20, 2021
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Abstract | References | Additional Information

Abstract: Let $X$ be a smooth, projective, rationally connected variety, defined over a number field $k$, and let $Z\subset X$ be a closed subset of codimension at least two. In this paper, for certain choices of $X$, we prove that the set of $Z$-integral points is potentially Zariski dense, in the sense that there is a finite extension $K$ of $k$ such that the set of points $P\in X(K)$ that are $Z$-integral is Zariski dense in $X$. This gives a positive answer to a question of Hassett and Tschinkel from 2001.

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Additional Information

David McKinnon
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
MR Author ID: 667698

Mike Roth
Affiliation: Department of Mathematics and Statistics, Queens University, Kingston, Ontario, Canada
MR Author ID: 717200
ORCID: 0000-0002-1182-9602

Received by editor(s): February 11, 2020
Received by editor(s) in revised form: September 28, 2020, January 24, 2021, and February 2, 2021
Published electronically: December 20, 2021
Additional Notes: The first and second authors were partially supported by NSERC research grants.
Article copyright: © Copyright 2021 University Press, Inc.