On plane sextics with double singular points

TL;DR

This paper computes the fundamental groups of five specific plane sextic curves with double singular points, confirming expected groups in most cases and demonstrating an approach applicable to similar curves.

Contribution

It introduces a method for computing fundamental groups of sextic curves with double singular points, applicable to other cases given their equations.

Findings

Four of the five fundamental groups match expectations

The approach is adaptable to other sextics with known equations

Provides explicit fundamental groups for five maximally singular sextics

Abstract

We compute the fundamental groups of five maximizing sextics with double singular points only; in four cases, the groups are as expected. The approach used would apply to other sextics as well, given their equations.