Calabi–Yau threefolds obtained as fiber products of elliptic and quasi-elliptic rational surfaces

Let X be a Calabi–Yau threefold defined over an algebraically closed field k of characteristic p>0. It is natural to expect that X has some properties which cannot be seen in characteristic zero. To observe such phenomena, we study Calabi–Yau threefolds constructed from fiber products of elliptic and quasi-elliptic rational surfaces over image. These Calabi–Yau threefolds turn out to be unirational, have fibrations which are not generically smooth. We shall also observe their Artin–Mazur formal groups and the Hodge duality.