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

Published:2005-06-01
Printed: Jun 2005
• Sławomir Cynk
• Christian Meyer
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## Abstract

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.
 Keywords: Calabi--Yau, double coverings, modular forms
 MSC Classifications: 14G10 - Zeta-functions and related questions [See also 11G40] (Birch-Swinnerton-Dyer conjecture) 14J32 - Calabi-Yau manifolds