On generalized hypergeometric equations and mirror maps

Abstract

This paper deals with generalized hypergeometric differential equations of order n ≥ 3 n \geq 3 having maximal unipotent monodromy at 0 0 . We show that among these equations those leading to mirror maps with integral Taylor coefficients at 0 0 (up to simple rescaling) have special parameters, namely R R -partitioned parameters. This result yields the classification of all generalized hypergeometric differential equations of order n ≥ 3 n \geq 3 having maximal unipotent monodromy at 0 0 such that the associated mirror map has the above integrality property.