ZETA-FUNCTIONS OF CERTAIN K3-FIBERED CALABI–YAU THREEFOLDS

We consider certain K3-fibered Calabi–Yau threefolds. One class of such Calabi–Yau threefolds is constructed by Hunt and Schimmrigk using twist maps. They are realized in weighted projective spaces as orbifolds of hypersurfaces. Our main goal of this paper is to investigate arithmetic properties of these K3-fibered Calabi–Yau threefolds. In particular, we give detailed discussions on the construction of these Calabi–Yau varieties, singularities and their resolutions. We then determine the zeta-functions of these Calabi–Yau varieties. Next we consider deformations of our K3-fibered Calabi–Yau threefolds, and we study the variation of the zeta-functions using p-adic rigid cohomology theory.