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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 3, Issue 2


Multiple prime covers of the riemann sphere

Aaron Wootton
Published Online: 2005-06-01 | DOI: https://doi.org/10.2478/BF02479202


A compact Riemann surface X of genus g≥2 which admits a cyclic group of automorphisms C q of prime order q such that X/C q has genus 0 is called a cyclic q-gonal surface. If a q-gonal surface X is also p-gonal for some prime p≠q, then X is called a multiple prime surface. In this paper, we classify all multiple prime surfaces. A consequence of this classification is a proof of the fact that a cyclic q-gonal surface can be cyclic p-gonal for at most one other prime p.

Keywords: Automorphism group; compact Riemann surface; hyperelliptic curve

Keywords: 14H30; 14H37; 30F10; 30F60; 20H10

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About the article

Published Online: 2005-06-01

Published in Print: 2005-06-01

Citation Information: Open Mathematics, Volume 3, Issue 2, Pages 260–272, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/BF02479202.

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© 2005 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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