A classification of the irreducible algebraic A-hypergeometric functions associated to planar point configurations

Abstract

We consider A-hypergeometric functions associated to normal sets in the plane. We give a classification of all point configurations for which there exists a parameter vector such that the associated hypergeometric function is algebraic. In particular, we show that there are no irreducible algebraic functions if the number of boundary points is sufficiently large and A is not a pyramid.