Some classes satisfying the 2-dimensional Jacobian conjecture and a proof of the complex conjecture until degree 104
Algebraic Geometry
2025-03-28 v5
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.
Keywords
Cite
@article{arxiv.1902.05923,
title = {Some classes satisfying the 2-dimensional Jacobian conjecture and a proof of the complex conjecture until degree 104},
author = {Thuy Nguyen},
journal= {arXiv preprint arXiv:1902.05923},
year = {2025}
}