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

Abstract

Let $X$ be a compact Riemann surface of genus $g\ge 2$. 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.

arXiv commentfinal version, 9 pages, minor improvements, added 2 references

References in corpus (1)

• The Full Automorphism Group of a Cyclic $p$-gonal Surface

Cited by in corpus (2)

• A family of $(p,n)$-gonal Riemann surfaces with several $(p,n)$-gonal groups
• Nilpotent groups of automorphisms of families of Riemann surfaces