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Vol. 51 No. 3–4 (2025)
Serdica Mathematical Journal

Articles

On the shape of a counterexample to the two-dimensional Jacobian conjecture

https://doi.org/10.55630/serdica.2025.51.299-314

Published 23-12-2025

  • Leonid Makar-Limanov

Leonid Makar-Limanov
Wayne State University, Detroit, USA

Abstract

Polynomials \(f, \ g \in \mathbb{C}[x,y]\) is a Jacobian pair if the Jacobian \({\rm J}(f,g) = 1\). The Jacobian conjecture (JC) formulated by O. H. Keller states that then \(\mathbb{C}[f,g] = \mathbb{C}[x,y]\). In this paper further information on the shape of the Newton polygon of \(f\) if the pair \(f, \ g\) is a counterexample to JC is obtained.

2020 Mathematics Subject Classification:

14R15, 14M25

Keywords

Jacobian conjecture, Newton polygon, leading forms

Full text

Author Details

Leonid Makar-Limanov

Department of Mathematics,
Wayne State University,
Detroit, MI 48202, USA
and
Department of Mathematics & Computer Science,
the Weizmann Institute of Science,
Rehovot 76100, Israel
e-mail: lml@wayne.edu

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