Sur les fonctions \`a singularit\'e de dimension 1

TL;DR

This paper extends previous results on holomorphic germs with one-dimensional singularities to all such germs, broadening the applicability of earlier findings.

Contribution

It generalizes earlier results from a specific class to all holomorphic germs with one-dimensional singularities.

Findings

Results valid for a large class now hold for all such germs.

The generalization confirms the robustness of previous theorems.

Implications for the study of singularities in complex analysis.

Abstract

In this article we show that all results proved for a large class of holomorphic germs $f : (\mathbb{C}^{n+1}, 0) \to (\mathbb{C}, 0)$ with a 1-dimension singularity in [B.II] are valid for an arbitrary such germ.