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arXiv · 1203.4053

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

Andreas Schweizer
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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.

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Andreas Schweizer. 2012-03-19. On the uniqueness of $(p,h)$-gonal automorphisms of Riemann surfaces. https://doi.org/10.1007/s00013-012-0397-8

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