Singularities of hypergeometric functions in several variables

Abstract

This paper deals with singularities of nonconfluent hypergeometric functions in several complex variables. Typically such a function is a multi-valued analytic function with singularities along an algebraic hypersurface. We describe such hypersurfaces in terms of the amoebas and the Newton polytopes of their defining polynomials. In particular, we show that the amoebas of classical discriminantal hypersurfaces are solid, that is, they possess the minimal number of complement components.