Dihedral coverings of trigonal curves

TL;DR

This paper classifies trigonal curves in Hirzebruch surfaces with dihedral Galois coverings and derives restrictions on the fundamental group of certain plane curves with high-multiplicity singular points.

Contribution

It provides a classification of trigonal curves with dihedral coverings and links these to fundamental group restrictions of plane curves with specific singularities.

Findings

Classification of trigonal curves with dihedral Galois coverings

Restrictions on fundamental groups of plane curves with high-multiplicity singularities

Insights into the structure of plane curves in algebraic geometry

Abstract

We classify and study trigonal curves in Hirzebruch surfaces admitting dihedral Galois coverings. As a consequence, we obtain certain restrictions on the fundamental group of a plane curve~$D$ with a singular point of multiplicity $(\deg D-3)$.