The Borcea-Voisin construction is a procedure allowing to construct a Calabi-Yau manifold starting from Calabi-Yau manifolds of lower dimension. After an introduction on the original construction, we will focus on one of its generalizations.
In particular, we will construct explicit examples of elliptic Calabi-Yau fourfolds, starting from a pair of K3 surfaces: the first being a double cover of a del Pezzo surface, and the second carrying an elliptic fibration. It is possible to describe the elliptic fibres in detail, showing the link between this fibration and the one we started with. Finally, we will show that these varieties have in a very natural way other fibrations.