Geometry and Arithmetic of certain Double Octic Calabi-Yau Manifolds

S. Cynk; C. Meyer

Geometry and Arithmetic of certain Double Octic Calabi-Yau Manifolds

Algebraic Geometry 2009-12-15 v1

Authors: S. Cynk , C. Meyer

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.

Keywords

Calabi-Yau manifolds double octics octic surface Hodge numbers rigid Calabi-Yau modularity conjecture algebraic geometry

Cite

@article{arxiv.math/0304121,
  title  = {Geometry and Arithmetic of certain Double Octic Calabi-Yau Manifolds},
  author = {S. Cynk and C. Meyer},
  journal= {arXiv preprint arXiv:math/0304121},
  year   = {2009}
}

Comments

16 pages, 5 figures

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