Symmetries of quasiplatonic Riemann surfaces

  • Gareth A. Jones

    University of Southampton, UK
  • David Singerman

    University of Southampton, UK
  • Paul D. Watson

    Peter Symonds College, Winchester, UK


We state and prove a corrected version of a theorem of Singerman, which relates the existence of symmetries (anticonformal involutions) of a quasiplatonic Riemann surface S\mathcal S (one uniformised by a normal subgroup NN of finite index in a cocompact triangle group Δ\Delta) to the properties of the group G=Δ/NG=\Delta/N. We give examples to illustrate the revised necessary and sufficient conditions for the existence of symmetries, and we relate them to properties of the associated dessins d'enfants, or hypermaps.

Cite this article

Gareth A. Jones, David Singerman, Paul D. Watson, Symmetries of quasiplatonic Riemann surfaces. Rev. Mat. Iberoam. 31 (2015), no. 4, pp. 1403–1414

DOI 10.4171/RMI/873