JournalsrmiVol. 24, No. 2pp. 391–405

On the number of ovals of a symmetry of a compact Riemann surface

  • Emilio Bujalance

    UNED, Madrid, Spain
  • José Manuel Gamboa

    Universidad Complutense de Madrid, Spain
  • Francisco Javier Cirre

    UNED, Madrid, Spain
  • Grzegorz Gromadzki

    University of Gdańsk, Poland
On the number of ovals of a symmetry of a compact Riemann surface cover
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Abstract

Let XX 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 XX in terms of few data of the monodromy of the covering XX/GX\rightarrow X/G, where G=\mboxAut\/±XG=\mbox{\rm Aut\/}^\pm X is the full group of conformal and anticonformal automorphisms of XX.

Cite this article

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. 391–405

DOI 10.4171/RMI/540