Geography of irreducible plane sextics

TL;DR

This paper classifies irreducible singular plane sextic curves based on their deformation types and computes the fundamental groups of their complements, advancing understanding in algebraic geometry.

Contribution

It completes the classification of irreducible singular plane sextics and calculates fundamental groups for most maximizing cases, filling gaps in existing literature.

Findings

Complete classification of irreducible singular plane sextics.

Fundamental groups computed for nearly all maximizing sextics.

Enhanced understanding of the topology of plane sextic complements.

Abstract

We complete the equisingular deformation classification of irreducible singular plane sextic curves. As a by-product, we also compute the fundamental groups of the complement of all but a few maximizing sextics.