Resumen de Symmetries of quasiplatonic Riemann surfaces

Gareth A. Jones, David Singerman , Paul Watson

• 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 (one uniformised by a normal subgroup N of finite index in a cocompact triangle group Δ) to the properties of the group G=Δ/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.