On lifting the hyperelliptic involution
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- by Robert D. M. Accola
- Proc. Amer. Math. Soc. 122 (1994), 341-347
- DOI: https://doi.org/10.1090/S0002-9939-1994-1197530-1
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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.References
- Robert D. M. Accola, Riemann surfaces with automorphism groups admitting partitions, Proc. Amer. Math. Soc. 21 (1969), 477–482. MR 237764, DOI 10.1090/S0002-9939-1969-0237764-9 F. Enriques, Sopra le superficie che posseggono un fascio ellittice o di genese due di curve razionli, Roma Reale Acad. Lincei, Rendiconti (5) 7 (1898), 281-286.
- H. M. Farkas, Automorphisms of compact Riemann surfaces and the vanishing of theta constants, Bull. Amer. Math. Soc. 73 (1967), 231–232. MR 213547, DOI 10.1090/S0002-9904-1967-11694-X
- H. M. Farkas, Unramified double coverings of hyperelliptic surfaces, J. Analyse Math. 30 (1976), 150–155. MR 437741, DOI 10.1007/BF02786710
- H. M. Farkas, Unramified coverings of hyperelliptic Riemann surfaces, Complex analysis, I (College Park, Md., 1985–86) Lecture Notes in Math., vol. 1275, Springer, Berlin, 1987, pp. 113–130. MR 922295, DOI 10.1007/BFb0078347
- Ryutaro Horiuchi, Normal coverings of hyperelliptic Riemann surfaces, J. Math. Kyoto Univ. 19 (1979), no. 3, 497–523. MR 553229, DOI 10.1215/kjm/1250522375
- C. Maclachlan, Smooth coverings of hyperelliptic surfaces, Quart. J. Math. Oxford Ser. (2) 22 (1971), 117–123. MR 283194, DOI 10.1093/qmath/22.1.117
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 341-347
- MSC: Primary 14H30; Secondary 14H45, 30F99
- DOI: https://doi.org/10.1090/S0002-9939-1994-1197530-1
- MathSciNet review: 1197530