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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On lifting the hyperelliptic involution

Author: Robert D. M. Accola
Journal: Proc. Amer. Math. Soc. 122 (1994), 341-347
MSC: Primary 14H30; Secondary 14H45, 30F99
MathSciNet review: 1197530
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Abstract: Let $ {W_p}$ stand for a compact Riemann surface of genus p.

(1) Let $ {W_q}$ be hyperelliptic, and let n be a positive integer. Then there exists an unramified covering of n sheets, $ {W_p} \to {W_q}$, where $ {W_p}$ is hyperelliptic.

(2) Let $ {W_{2n + 1}} \to {W_2}$ be an unramified Galois covering with a dihedral group as Galois group, and let n be odd. Then $ {W_{2n + 1}}$ is elliptic hyperelliptic (bi-elliptic).

(3) Let $ {W_4} \to {W_2}$ be an unramified non-Galois covering of three sheets. Then $ {W_4}$ is hyperelliptic.

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Additional Information

PII: S 0002-9939(1994)1197530-1
Article copyright: © Copyright 1994 American Mathematical Society

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