Cyclic curves over the reals

TL;DR

This paper investigates the automorphism groups of real cyclic p-gonal curves, focusing on cases where the curves admit a regular meromorphic function of degree p, extending previous work on hyperelliptic curves.

Contribution

The paper extends the classification of automorphism groups to real cyclic p-gonal curves for arbitrary prime p, generalizing known results for hyperelliptic cases.

Findings

Automorphism groups characterized for real cyclic p-gonal curves

Extension of hyperelliptic automorphism classifications to higher p

New structural insights into real algebraic curves

Abstract

In this paper we study the automorphism groups of real curves admitting a regular meromorphic function $f$ of degree $p$, so called real cyclic $p$-gonal curves. When $p=2$ the automorphism groups of real hyperelliptic curves where given by Bujalance et al. in \cite{BCGG}.