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

[摘要] We study Calabi--Yau manifolds constructed as double coverings of$mathbb{P}^3$ branched along an octic surface. We give a list of 87examples corresponding to arrangements of eight planes defined over$mathbb{Q}$. The Hodge numbers are computed for all examples. There are10 rigid Calabi--Yau manifolds and 14 families with $h^{1,2}=1$. Themodularity conjecture is verified for all the rigid examples.

[学科分类] 数学（综合）

[关键词] Calabi--Yau;double coverings;modular forms