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Geometry and Arithmetic of Certain Double Octic Calabi–Yau Manifolds

Published online by Cambridge University Press:  20 November 2018

Sławomir Cynk  and
Christian Meyer
Sławomir Cynk
Affiliation:
Instytut Matematyki, Uniwersytetu Jagiellońskiego, ul. Reymonta 4, 30–059 Kraków, Poland e-mail: [email protected]
Christian Meyer
Affiliation:
Fachbereich Mathematik und Informatik, Johannes Gutenberg-Universität, Staudingerweg 9, D–55099 Mainz, Germany e-mail: [email protected]
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Abstract

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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

14G1014J32Calabi–Yaudouble coveringsmodular forms
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 2 , 01 June 2005 , pp. 180 - 194
Copyright
Copyright © Canadian Mathematical Society 2005

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