Resumen de Geometry and Arithmetic of Certain Double Octic Calabi-Yau Manifolds

Slawomir Cynk, Christian Meyer

• We study Calabi¿Yau manifolds constructed as double coverings of mathbb{P}3 branched along an octic surface. We give a list of 87 examples corresponding to arrangements of eight planes defined over mathbb{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.