Fundamental groups of symmetric sextics. II

TL;DR

This paper investigates the fundamental groups of specific plane sextic curves, particularly of torus type with certain singularities, revealing that these groups are the simplest possible, such as * and .

Contribution

It computes the fundamental groups of plane sextics of torus type with particular singularities and other sextics, identifying them as the simplest possible groups.

Findings

Fundamental groups for sextics with  and  singularities are * and .

Computed fundamental groups for various sextics, both of and not of torus type.

Groups found are the simplest possible, indicating fundamental group simplicity.

Abstract

We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with the set of inner singularities $2\bold{A}_8$ or $\bold{A}_{17}$. We also compute the fundamental groups of a number of other sextics, both of and not of torus type. The groups found are simplest possible, i.e., $\Bbb{Z}_2*\Bbb{Z}_3$ and $\Bbb{Z}_6$, respectively.