Unramified double coverings of hyperelliptic surfaces. II

Farkas, H. M.

doi:10.1090/S0002-9939-1987-0908651-6

Unramified double coverings of hyperelliptic surfaces. II

Author: H. M. Farkas
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
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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.

[B] E. Bujalance, A classification of unramified double coverings of hyperelliptic Riemann surfaces, Arch. Math. (Basel) 47 (1986), no. 1, 93–96. MR 855143, https://doi.org/10.1007/BF01202505
[F1] H. M. Farkas, Unramified double coverings of hyperelliptic surfaces, J. Analyse Math. 30 (1976), 150–155. MR 437741, https://doi.org/10.1007/BF02786710
[F2] -, Unramified coverings of hyperelliptic Riemann surfaces (Preprint).
[FK] Hershel M. Farkas and Irwin Kra, Riemann surfaces, Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York-Berlin, 1980. MR 583745
[M] C. Maclachlan, Smooth coverings of hyperelliptic surfaces, Quart. J. Math. Oxford Ser. (2) 22 (1971), 117–123. MR 283194, https://doi.org/10.1093/qmath/22.1.117