# Parametrization simple irreducible plane curve singularities in arbitrary characteristic

## TL;DR

This paper classifies parametrization simple irreducible plane curve singularities in any characteristic, providing bounds and explicit normal forms, extending previous characteristic-zero results to arbitrary characteristic.

## Contribution

It introduces a bound for determinacy based on the conductor and offers a complete classification with explicit normal forms in arbitrary characteristic.

## Key findings

- Bound for determinacy in terms of conductor
- Complete list of normal forms for parametrization simple singularities
- Extension of classification from characteristic zero to arbitrary characteristic

## Abstract

We study the classification of plane curve singularities in arbitrary characteristic. We first give a bound for the determinacy of a plane curve singularity with respect to pararametrization equivalence in terms of its conductor. Then we classify parametrization simple plane curve singularities which are irreducible by giving a concrete list of normal forms of equations and parametrizations. In characteristic zero, the classification of parametrization simple irreducible plane curve singularities was achieved by Bruce and Gaffney.