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

2020/02/12 by McKinnon, David, Roth, Mike
#11G35 #14G05 #14GM22 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.04961

Abstract

Let V be a smooth, projective, rationally connected variety, defined over a number field k, and let Z⊂ V be a closed subset of codimension at least two. In this paper, for certain choices of V, 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∈ V(K) that are Z-integral is Zariski dense in V. This gives a positive answer to a question of Hassett and Tschinkel from 2001.

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