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

http://dx.doi.org/10.4153/CMB-2005-016-7
Canad. Math. Bull. 48(2005), 180-194

  Published:2005-06-01
 Printed: Jun 2005

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 $h^{1,2}=1$. The modularity conjecture is verified for all the rigid examples.