Topology of plane algebraic curves: the algebraic approach

TL;DR

This paper reviews key tools, results, and open problems related to the classification and topology of plane sextic and trigonal curves within algebraic geometry.

Contribution

It provides an overview of the algebraic methods used to analyze the topology of specific plane algebraic curves and highlights open research questions.

Findings

Summary of principal tools and results

Identification of open problems in classification

Insights into algebraic topology of plane curves

Abstract

We discuss the principle tools and results and state a few open problems concerning the classification and topology of plane sextics and trigonal curves in ruled surfaces.