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

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

2012-03-19

arxiv.org/abs/1203.4053v1

Mathematics

Complex Variables

8 pages

Scientific paper

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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