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.

16 pages, 5 figures

References in corpus (1)

• Calabi-Yau threefolds with a curve of singularities and counterexamples to the Torelli problem