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

Canadian mathematical bulletin

关键词: Calabi--Yau;    double coverings;    modular forms;   

DOI  :  10.4153/CMB-2005-016-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 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.

【 授权许可】

Unknown