On the Zariski invariant of plane branches

TL;DR

This paper introduces a method to compute the Zariski invariant of plane branches using contact order and intersection multiplicity with specific curves, providing new insights into their geometric properties.

Contribution

It presents a novel approach to determine the Zariski invariant through intersection theory, enhancing understanding of plane branches in algebraic geometry.

Findings

Method to compute Zariski invariant using contact order

Relation between intersection multiplicity and Zariski invariant

Implications for classification of plane branches

Abstract

We show how to obtain the Zariski invariant of a plane branch employing the contact order or the intersection multiplicity with elements in a particular family of curves and we present some consequences of this result.