Let be a symmetric compact Riemann surface whose full group of conformal automorphisms is cyclic. We derive a formula for counting the number of ovals of the symmetries of in terms of few data of the monodromy of the covering , where is the full group of conformal and anticonformal automorphisms of .
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Emilio Bujalance, José Manuel Gamboa, Francisco Javier Cirre, Grzegorz Gromadzki, On the number of ovals of a symmetry of a compact Riemann surface. Rev. Mat. Iberoam. 24 (2008), no. 2, pp. 391–405DOI 10.4171/RMI/540