Periods of Hodge cycles and special values of the Gauss' hypergeometric function

2020/10/01 by Jorge Duque Franco, Franco, Jorge Duque
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · doi:10.48550/arxiv.2010.00707

openalex publication_date 2020/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute periods of perturbations of a Fermat variety. This allows us to consider a subspace of the Hodge cycles defined by "simple" arithmetic conditions. We explore some examples and give an upper bound for the dimension of this subspace. As an application, we find explicit expressions involving some Gauss' hypergeometric functions which are algebraic over the field of rational functions in one variable.

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