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Geometry and Arithmetic of certain Double Octic Calabi-Yau Manifolds

S. Cynk·C. Meyer
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Abstract

We study Calabi-Yau manifolds constructed as double covers of ${\mathbb P}^3$ branched along an octic surface. We give a list of 85 examples corresponding to arrangements of eight planes defined over ${\mathbb Q}$. The Hodge numbers are computed for all examples. There are 7 rigid Calabi-Yau manifolds and 14 families with $h^{1,2}=1$. The modularity conjecture is verified for all the rigid examples.

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S. Cynk, C. Meyer. 2003-04-09. Geometry and Arithmetic of certain Double Octic Calabi-Yau Manifolds. https://arxiv.org/abs/math/0304121

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