Plane Jacobian Conjecture for rational polynomials

TL;DR

This paper investigates the invertibility of polynomial maps with constant Jacobian determinants in the complex plane, focusing on cases where the component polynomials are rational.

Contribution

It establishes conditions under which rational polynomial maps with constant Jacobian are invertible, advancing understanding of the Jacobian conjecture for rational functions.

Findings

Rational polynomial maps with constant Jacobian are invertible under certain conditions.

Provides new criteria for invertibility of rational polynomial maps.

Contributes to the broader Jacobian conjecture in complex algebraic geometry.

Abstract

A non-zero constant Jacobian polynomial maps $F=(P,Q)$ of $\mathbb{C}^2$ is invertible if $P$ and $Q$ are rational polynomials.