Normal forms for hypersurface singularities

TL;DR

This paper introduces a method to derive normal forms for hypersurface singularities in complex spaces using holomorphic vector fields, aiding in the classification and analysis of such singularities.

Contribution

It presents a novel approach to normal forms for hypersurface singularities leveraging holomorphic vector fields, advancing the understanding of their local structure.

Findings

Normal forms for hypersurface singularities are established.

Holomorphic vector fields are effectively used to simplify singularity descriptions.

The method improves classification of complex hypersurface singularities.

Abstract

We provide normal forms for singularities of analytic hypersurfaces in $({\mathbb C}^n,0)$, using holomorphic vector fields.