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Mathematics > Algebraic Geometry

arXiv:1806.03180 (math)
[Submitted on 8 Jun 2018]

Title:The arithmetic puncturing problem and integral points

Authors:David McKinnon, Yi Zhu
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Abstract:In this paper, we provide evidence to support a positive answer to a question of Hassett and Tschinkel. In particular, if an algebraic variety V has a dense set of rational points, they ask whether or not the set of D-integral points is potentially dense, where D is a set of codimension at least two. We give a positive answer to this question in many cases, including varieties whose generic linear section is a smooth rational curve, and certain K3 surfaces. We also discuss some stronger notions of integrality of points, and give some positive answers to some cases of the analogous question in the stronger context.
Comments: 10 pages, no figures
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
Cite as: arXiv:1806.03180 [math.AG]
  (or arXiv:1806.03180v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1806.03180

Submission history

From: David McKinnon [view email]
[v1] Fri, 8 Jun 2018 14:26:23 UTC (9 KB)
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