The Tjurina number of a plane curve with two branches and high intersection multiplicity

TL;DR

This paper introduces a family of plane curves with two branches that maintain a constant Tjurina number within their equisingularity class, providing a formula based on topological data.

Contribution

It presents a new family of plane curves with fixed Tjurina number and derives a closed-form formula relating it to topological invariants.

Findings

Constant Tjurina number within the family of curves.

Derived a closed formula for the Tjurina number.

Applicable to curves with high intersection multiplicity.

Abstract

In this paper we provide a family of reduced plane curves with two branches that have a constant Tjurina number in their equisingularity class, along with a closed formula for it in terms of topological data.