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

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