On the uniqueness of $(p,h)$-gonal automorphisms of Riemann surfaces

TL;DR

This paper proves that for a compact Riemann surface of genus at least 2, a properly $(p,h)$-gonal automorphism subgroup of prime order greater than $6h+6$ is unique, contributing to the understanding of automorphism group structures.

Contribution

It establishes a new uniqueness criterion for properly $(p,h)$-gonal automorphisms when the prime order exceeds $6h+6$, expanding previous results in the field.

Findings

Properly $(p,h)$-gonal subgroups are unique if $p>6h+6$.

The paper discusses related automorphism group properties.

Provides conditions for automorphism subgroup uniqueness.

Abstract

Let $X$ be a compact Riemann surface of genus $g\geq 2$. A cyclic subgroup of prime order $p$ of $Aut(X)$ is called properly $(p,h)$-gonal if it has a fixed point and the quotient surface has genus $h$. We show that if $p>6h+6$, then a properly $(p,h)$-gonal subgroup of $Aut(X)$ is unique. We also discuss some related results.