Hypergeometric series and Hodge cycles of four dimensional cubic hypersurfaces
Algebraic Geometry
2007-05-23 v2 Number Theory
Abstract
In this article we find connections between the values of Gauss hypergeometric functions and the dimension of the vector space of Hodge cycles of four dimensional cubic hypersurfaces. Since the Hodge conjecture is well-known for those varieties we calculate values of Hypergeometric series on certain points. Our methods is based on the calculation of the Picard-Fuchs equations in higher dimensions, reducing them to the Gauss equation and then applying the Abelian Subvariety Theorem to the corresponding hypergeometric abelian varieties.
Keywords
Cite
@article{arxiv.math/0507436,
title = {Hypergeometric series and Hodge cycles of four dimensional cubic hypersurfaces},
author = {Hossein Movasati and Stefen Reiter},
journal= {arXiv preprint arXiv:math/0507436},
year = {2007}
}