Hypergeometric series and Hodge cycles of four dimensional cubic hypersurfaces

Details Hypergeometric series and Hodge cycles of four dimensional cubic hypersurfaces Hypergeometric series and Hodge cycles of four dimensional cubic hypersurfaces

2005-07-21

arxiv.org/abs/math/0507436v2

International Journal of number theory, vol 2, No 6, 1--20, 2006

Mathematics

Algebraic Geometry

Scientific paper

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 $CM$ 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.

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