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

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

2006-02-10

arxiv.org/abs/math/0602205v3

Journal of Algebra, Volume 312, Issue 1, 1 June 2007, Pages 377-396

Mathematics

Algebraic Geometry

18 pages, 5 figures

Scientific paper

10.1016/j.jalgebra.2007.01.018

If $p$ is prime, a compact Riemann surface $X$ of genus $g\geq 2$ is called cyclic $p$-gonal if it admits a cyclic group of automorphisms $C_{p}$ of order $p$ such that the quotient space $X/C_{p}$ has genus 0. If in addition $C_{p}$ is not normal in the full automorphism $G$, then we call $G$ a non-normal cyclic $p$-gonal group. In the following we classify all non-normal $p$-gonal groups.

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