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Geometry and Arithmetic of Certain Double Octic Calabi–Yau Manifolds
Published online by Cambridge University Press: 20 November 2018
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.
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- Copyright © Canadian Mathematical Society 2005
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