Fundamental groups of symmetric sextics

TL;DR

This paper investigates the fundamental groups of specific plane sextic curves with multiple singularities, expanding the understanding of their topological properties and providing new computations for a broad class of sextics.

Contribution

It introduces methods to compute fundamental groups of sextics with multiple singularities and presents new results for 125 previously unstudied cases.

Findings

Computed fundamental groups for sextics with multiple E6 singularities.

Established moduli space structures for these sextics.

Provided new fundamental group examples for complex plane curves.

Abstract

We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with at least two type $\bold{E}_6$ singular points. As a simple application, we compute the fundamental groups of 125 other sextics, most of which are new.