Pencils and Infinite Dihedral covers of P^2

TL;DR

This paper explores the relationship between dihedral covers of the projective plane, ramification along algebraic curves, and pencils of curves containing those curves, revealing new insights into their interconnected structures.

Contribution

It establishes novel links between finite and infinite dihedral covers of the projective plane and the geometry of pencils of curves containing a given algebraic curve.

Findings

Connection between dihedral covers and pencils of curves

Characterization of ramification along algebraic curves

Insights into the structure of infinite dihedral covers

Abstract

In this work we study the connection between the existence of finite dihedral covers of the projective plane ramified along an algebraic curve C, infinite dihedral covers, and pencils of curves containing C.