One branch curve singularities with at most 2-parameter families of ideals

TL;DR

This paper provides a criterion to identify one branch curve singularities with at most 2-parameter families of ideals, listing minimal examples from Arnold's classification.

Contribution

It introduces a specific criterion and identifies minimal singularities with limited ideal families within the classification.

Findings

List of singularities with at most 2-parameter ideal families

Criterion for identifying such singularities

Minimal examples from Arnold's classification

Abstract

A criterion is given in order that the ideals of a one branch curve singularity form at most 2-parameter families. Namely, we present a list of plane curve singularities from the Arnold's classification which are the smallest among all one branch singularities having at most 2-parameter families of ideals.