Discriminant amoebas and lopsidedness

Abstract

We study amoebas of the principal $A$-determinant in relationship with the lopsidedness condition: the (co)amoeba of the principal $A$-determinant stratifies the space of lopsided (co)amoebas according to equivalence of order maps — a refinement of topological equivalence. We extend Nilsson and Passare’s description of the coamoeba of the $A$-discriminant to the case when $A$ defines a projective toric curve. As an application, we compute coefficients of transition matrices necessary when gluing local monodromy groups of $A$-hypergeometric systems.