Geometry and Arithmetic of certain Double Octic Calabi-Yau Manifolds

Details Geometry and Arithmetic of certain Double Octic Calabi-Yau Manifolds Geometry and Arithmetic of certain Double Octic Calabi-Yau Manifolds

2003-04-09

arxiv.org/abs/math/0304121v1

Canadian Math. Bull. 48, no. 2 (2005), pp. 180-194

Mathematics

Algebraic Geometry

16 pages, 5 figures

Scientific paper

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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