Zeta-functions of certain K3 fibered Calabi--Yau threefolds

Details Zeta-functions of certain K3 fibered Calabi--Yau threefolds Zeta-functions of certain K3 fibered Calabi--Yau threefolds

2009-11-04

arxiv.org/abs/0911.0783v1

Mathematics

Number Theory

55 pages, 10 figures, submitted for publication

Scientific paper

We consider certain $K3$-fibered Calabi--Yau threefolds. One class of such Calabi--Yau threefolds are 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 Calabi--Yau threefolds. We also consider deformations of our Calabi--Yau threefolds, and we study the variation of the zeta-functions using $p$-adic rigid cohomology theory.

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