The Newton complementary dual revisited

TL;DR

This paper revisits the Newton complementary duality, providing a conceptual revision that simplifies understanding of rational maps and their images, and introduces a ring-homomorphism for comparing graphs of dual maps.

Contribution

It offers a new conceptual framework for Newton duality, simplifying existing statements and introducing a ring-homomorphism to compare rational maps and their Newton duals.

Findings

Simplified the conceptual understanding of Newton duality.

Introduced a ring-homomorphism for graph comparison.

Enhanced the analysis of rational maps and their images.

Abstract

This work deals with the notion of Newton complementary duality as raised originally in the work of the second author and B. Costa. A conceptual revision of the main steps of the notion is accomplished which then leads to a vast simplification and improvement of several statements concerning rational maps and their images. A ring-homomorphism like map is introduced that allows for a close comparison between the respective graphs of a rational map and its Newton dual counterpart.