Geometry and Arithmetic of certain Double Octic Calabi-Yau Manifolds

Abstract

We study Calabi-Yau manifolds constructed as double covers of ${\mathbb P}^3$ branched along an octic surface. We give a list of 85 examples corresponding to arrangements of eight planes defined over ${\mathbb Q}$. The Hodge numbers are computed for all examples. There are 7 rigid Calabi-Yau manifolds and 14 families with $h^{1,2}=1$. The modularity conjecture is verified for all the rigid examples.