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

IF 0.9 1区 数学 Q2 MATHEMATICS
David McKinnon, Mike Roth
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引用次数: 0

Abstract

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

一些有理连通三重上的余维两个积分点是潜在稠密的
设X X是定义在数域k k上的光滑的、射影的、合理连通的变种,并设Z∧X Z\子集X是余维至少为2的闭子集。在本文中,对于X X的某些选择,我们证明了Z Z积分点的集合是潜在的Zariski稠密的,即K K的有限扩展K K使得点P∈X(K) P\ In X(K)是Z Z积分的集合P∈X(K) P\ In X(X)是Zariski稠密的。这对哈塞特和茨钦克尔2001年提出的一个问题给出了肯定的答案。
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来源期刊
CiteScore
2.70
自引率
5.60%
发文量
23
审稿时长
>12 weeks
期刊介绍: The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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