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

## TL;DR

This paper constructs specific polynomial maps to explore the Jacobian conjecture in two variables, proving it holds for degrees up to 104 in the complex case, thus extending previous known bounds.

## Contribution

It introduces new classes of polynomial maps satisfying the 2D Jacobian conjecture and improves the degree bound for the complex case from 100 to 104 using Newton polygon techniques.

## Key findings

- Identified classes of polynomial maps satisfying the Jacobian conjecture.
- Proved the conjecture holds for degrees up to 104 in the complex case.
- Extended the known degree bound from 100 to 104 since 1983.

## 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.