Multiple prime covers of the riemann sphere |
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Authors: | Aaron Wootton |
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Affiliation: | (1) Department of Mathematics, University of Arizona, 617 North Santa Rita, AZ85721 Tucson, USA |
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Abstract: | 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. |
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Keywords: | Automorphism group compact Riemann surface hyperelliptic curve |
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