Unramified double coverings of hyperelliptic surfaces. II
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- by H. M. Farkas PDF
- Proc. Amer. Math. Soc. 101 (1987), 470-474 Request permission
Abstract:
In this note we illustrate how to count the fixed points of a lift of the hyperelliptic involution to a smooth unramified double cover. In this way we obtain a new proof of the assertion that only $\left ( {\begin {array}{*{20}{c}} {2g + 2} \\ 2 \\ \end {array} } \right )$ of the double covers are hyperelliptic and classify the remaining covers in terms of $\tilde g$-hyperellipticity.References
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- H. M. Farkas, Unramified double coverings of hyperelliptic surfaces, J. Analyse Math. 30 (1976), 150–155. MR 437741, DOI 10.1007/BF02786710 —, Unramified coverings of hyperelliptic Riemann surfaces (Preprint).
- Hershel M. Farkas and Irwin Kra, Riemann surfaces, Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York-Berlin, 1980. MR 583745
- 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
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 470-474
- MSC: Primary 30F10; Secondary 14H30
- DOI: https://doi.org/10.1090/S0002-9939-1987-0908651-6
- MathSciNet review: 908651