A note on the integrality of mirror maps

2024/10/05 by Adolphson, Alan, Sperber, Steven
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2410.04293

Abstract

We give a class of examples of A-hypergeometric systems that display integrality of mirror maps. Specifically, these systems have solutions F(λ₁,…,λ_N) = 1 and logλ^l + G(λ₁,…,λ_N) (for certain l∈\mathbb Z^N) such that exp G(λ) has integral coefficients. The proof requires only some elementary congruences.

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