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1. CMB 2007 (vol 50 pp. 486)
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Higher-Dimensional Modular\\Calabi--Yau Manifolds We construct several examples of higher-dimensional Calabi--Yau manifolds and prove their
modularity.
Categories:14G10, 14J32, 11G40 |
2. CMB 2005 (vol 48 pp. 180)
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Geometry and Arithmetic of Certain Double Octic Calabi--Yau Manifolds 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:Calabi--Yau, double coverings, modular forms Categories:14G10, 14J32 |