Invariants of plane curve singularities and Newton diagrams

TL;DR

This paper introduces an intersection-theoretical method to compute invariants of plane curve singularities, providing explicit formulas and extending classical theorems to nondegenerate cases using Newton transformations.

Contribution

It offers new formulas for invariants like μ, δ, r of plane curve singularities via Newton transformations, enhancing understanding of their relationships.

Findings

Derived formulas for μ, δ, r invariants

Extended classical theorems to nondegenerate singularities

Provided a new intersection-theoretical framework

Abstract

We present an intersection-theoretical approach to the invariants of plane curve singularities $\mu$, $\delta$, $r$ related by the Milnor formula $2\delta=\mu+r-1$. Using Newton transformations we give formulae for $\mu$, $\delta$, $r$ which imply planar versions of well-known theorems on nondegenerate singularities.