Nearly irreducibility of polynomials and the Newton diagrams

TL;DR

This paper introduces a criterion based on Newton diagrams to determine when a polynomial in two complex variables is nearly irreducible, meaning its factors share a common zero.

Contribution

It provides a novel criterion for nearly irreducibility of polynomials using Newton diagrams, linking geometric and algebraic properties.

Findings

Criterion for nearly irreducibility based on Newton diagrams

Characterization of polynomial factors sharing common zeros

Connection between geometric diagrams and algebraic factorization

Abstract

Let f be a polynomial in two complex variables. We say that f is nearly irreducible if any two nonconstant polynomial factors of f have a common zero. In the paper we give a criterion of nearly irreducibility for a given polynomial f in terms of its Newton diagram.