# Lipschitz geometry of complex plane algebraic curves

## TL;DR

This paper classifies complex plane algebraic curves based on their Lipschitz geometry, considering the Euclidean metric and bilipschitz homeomorphisms, providing a comprehensive understanding of their geometric equivalence.

## Contribution

It offers a complete classification of complex plane algebraic curves under bilipschitz homeomorphisms, a novel geometric perspective.

## Key findings

- Classification of curves up to bilipschitz equivalence
- Identification of invariants under bilipschitz transformations
- Framework for comparing algebraic curves geometrically

## Abstract

We present a complete classification of complex plane algebraic curves, equipped with the induced Euclidean, up to global bilipschitz homeomorphism.