Plane sextics with a type $\mathbf{E}_6$ singular point

TL;DR

This paper classifies plane sextic curves with a specific singularity type and computes their fundamental groups, advancing understanding of their geometric and topological properties.

Contribution

It provides a classification up to equisingular deformation and calculates fundamental groups for these specialized sextic curves.

Findings

Classification of plane sextics with an E6 singularity

Computed fundamental groups of these sextics

Enhanced understanding of their deformation and topology

Abstract

We give a classification up to equisingular deformation and compute the fundamental groups of maximizing plane sextics with a type $\mathbf{E}_6$ singular point.