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Hypergeometric series and Hodge cycles of four dimensional cubic hypersurfaces

Research paper by Hossein Movasati, Stefen Reiter

Indexed on: 30 Aug '06Published on: 30 Aug '06Published in: Mathematics - Algebraic Geometry



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 $CM$ 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.