Invariance of the jacobian Newton diagram

TL;DR

This paper proves that the jacobian Newton diagram of a holomorphic map in two variables is determined solely by the equisingularity class of the pair of curves it defines, highlighting an invariance property.

Contribution

It establishes the invariance of the jacobian Newton diagram under equisingularity, linking geometric curve properties to algebraic invariants.

Findings

Jacobian Newton diagram depends only on equisingularity class

Invariance of the diagram under certain deformations

Provides a new tool for classifying curve singularities

Abstract

We prove that the jacobian Newton diagram of the holomorphic mapping $(f,g):(C^2,0)\to(C^2,0)$ depends only on the equisingularity class of the pair of curves $f=0$ and $g=0$.