# A discriminant criterion of irreducibility

## TL;DR

This paper introduces a new criterion for determining the irreducibility of complex power series in two variables using jacobian Newton diagrams, and explores the singularity at infinity of certain plane affine curves.

## Contribution

It presents a novel irreducibility criterion based on jacobian Newton diagrams and analyzes singularities at infinity for specific plane affine curves.

## Key findings

- Irreducibility criterion using jacobian Newton diagrams
- Analysis of singularities at infinity for plane affine curves
- Global implications of the irreducibility criterion

## Abstract

In this paper we give a criterion of irreducibility for a complex power series in two variables, using the notion of jacobian Newton diagrams, defined with respect to any direction. Moreover we study the singularity at infinity of a plane affine curve with one point at infinity for which the global counterpart of our main result holds.