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

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.