Coamoebas of polynomials supported on circuits

TL;DR

This paper explores the properties of coamoebas of polynomials supported on circuits, providing explicit descriptions, bounds, and relations to critical points and solutions, advancing understanding of their geometric and algebraic structure.

Contribution

It offers a comprehensive description of coamoebas supported on circuits, linking their topology to polynomial critical points and solutions, with new bounds and characterizations.

Findings

Explicit description of coamoeba space

Relation between coamoeba components and critical points

Upper bound on planar coamoeba area

Abstract

We study coamoebas of polynomials supported on circuits. Our results include an explicit description of the space of coamoebas, a relation between connected components of the coamoeba complement and critical points of the polynomial, an upper bound on the area of a planar coamoeba, and a recovered bound on the number of positive solutions of a fewnomial system.