Pinchuk Maps and Function Fields

TL;DR

This paper investigates Pinchuk maps related to the real Jacobian conjecture, revealing that their associated rational function field extensions of degree six lack nontrivial automorphisms, providing new insights into their algebraic structure.

Contribution

It demonstrates that all Pinchuk-type counterexamples have degree six rational function field extensions with trivial automorphism groups, a novel algebraic property.

Findings

Pinchuk maps have degree six function field extensions.

These extensions have no nontrivial automorphisms.

The result clarifies the algebraic structure of such counterexamples.

Abstract

All counterexamples of Pinchuk type to the strong real Jacobian conjecture are shown to have rational function field extensions of degree six with no nontrivial automorphisms.