A note on the integrality of mirror maps

Abstract

We give a class of examples of $A$-hypergeometric systems that display integrality of mirror maps. Specifically, these systems have solutions $F({\lambda }_1,\dots ,{\lambda }_N)=1$ and $\log {\lambda }^l+G({\lambda }_1,\dots ,{\lambda }_N)$ (for certain $l\in {\mathbb{Z}}^N$) such that $\exp G(\lambda )$ has integral coefficients. The proof requires only some elementary congruences.

7 pages