Work

Some classes satisfying the 2-dimensional Jacobian conjecture and a proof of the complex conjecture until degree 104

Year: 2025

Type: article

Abstract: We construct a non-proper set of two variables polynomial maps and study the nowhere vanishing Jacobian condition of the Jacobian conjecture for this set. We obtain some classes of polynomial maps satisfying the 2-dimensional Jacobian conjecture for both real and complex cases. In addition, by Newton polygon technique, we prove that the complex conjecture is true until degree 104, improving Moh boundary (degree 100) since 1983.

Source: Quaestiones Mathematicae

DOI: 10.2989/16073606.2025.2482655

Author: Thuy Nguyen

Institution: Universidade Estadual Paulista (Unesp)

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Universidade Federal de Uberlândia, Conselho Nacional de Desenvolvimento Científico e Tecnológico

Award: Polynomial mappings and Characteristic Classes of Singular Varieties