Invertible polynomial mappings via Newton non-degeneracy

TL;DR

This paper introduces a new Newton non-degeneracy condition to analyze invertible polynomial mappings, providing a sufficient criterion for the Jacobian problem across real, complex, and mixed cases.

Contribution

It establishes a novel Newton non-degeneracy condition that ensures invertibility of polynomial mappings, advancing understanding of the Jacobian problem.

Findings

Proves a sufficient condition for the Jacobian problem.

Analyzes the bifurcation locus under the new non-degeneracy condition.

Applies results to real, complex, and mixed polynomial mappings.

Abstract

We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.