Higher-dimensional Calabi-Yau varieties with dense sets of rational points

TL;DR

This paper constructs higher-dimensional Calabi-Yau varieties over number fields with dense rational points, providing elementary methods and specific examples, including threefolds with Enriques surfaces, demonstrating potential density.

Contribution

It introduces new constructions of Calabi-Yau varieties with dense rational points, including elementary and specialized threefold examples, advancing understanding of rational point distribution.

Findings

Constructed higher-dimensional Calabi-Yau varieties with dense rational points

Provided elementary constructions valid in arbitrary dimensions

Showed potential density for general members of the constructed families

Abstract

We construct higher-dimensional Calabi-Yau varieties defined over a given number field with Zariski dense sets of rational points. We give two elementary constructions in arbitrary dimensions as well as another construction in dimension three which involves certain Calabi-Yau threefolds containing an Enriques surface. The constructions also show that potential density holds for (sufficiently) general members of the families.