On polynomial mappings from the plane to the plane

TL;DR

This paper investigates polynomial mappings from the plane to the plane, introducing quadratic forms that help determine the number of positive and negative cusps of such mappings.

Contribution

It constructs quadratic forms whose signatures reveal the counts of positive and negative cusps in generic polynomial plane mappings.

Findings

Quadratic forms are constructed to analyze cusp counts.

Signatures of these forms determine positive and negative cusps.

Method provides a new algebraic approach to cusp enumeration.

Abstract

Let f be a generic polynomial mapping mapping from the plane to the plane. There are constructed quadratic forms whose signatures determine the number of positive and negative cusps of f.