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

  • Emilio Bujalance

    UNED, Madrid, Spain
  • Francisco Javier Cirre

    UNED, Madrid, Spain
  • José Manuel Gamboa

    Universidad Complutense de Madrid, Spain
  • Grzegorz Gromadzki

    University of Gdańsk, Poland

Abstract

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 .

Cite this article

Emilio Bujalance, Francisco Javier Cirre, José Manuel Gamboa, 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