Geometry and Arithmetic of Certain Double Octic Calabi–Yau Manifolds

Abstract

AbstractWe study Calabi–Yau manifolds constructed as double coverings of ℙ3 branched along an octic surface. We give a list of 87 examples corresponding to arrangements of eight planes defined over ℚ. The Hodge numbers are computed for all examples. There are 10 rigid Calabi–Yau manifolds and 14 families with h1,2 = 1. The modularity conjecture is verified for all the rigid examples.