Irreducibility criterion for singular hypersurfaces of $({\mathbb C}^n,0)$

TL;DR

This paper introduces an irreducibility criterion for hypersurfaces in complex space using vector fields and Weierstrass division, providing a new algebraic approach to understanding hypersurface singularities.

Contribution

It presents a novel irreducibility criterion based solely on vector fields and Weierstrass division, simplifying previous methods.

Findings

New criterion for hypersurface irreducibility

Applicable to singular hypersurfaces in complex space

Utilizes algebraic tools like Weierstrass division

Abstract

Using vector fields we obtain an irreducibility criterion for hypersurfaces. It only requires the Weierstrass division.