Symmetries of quasiplatonic Riemann surfaces

• Gareth A. Jones ^[1] ; David Singerman ^[1] ; Paul D. Watson ^[2]
  1. [1] University of Southampton

     University of Southampton

     GB.ENG.M4.24UJ, Reino Unido

     
  2. [2] Peter Symonds College
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 4, 2015, págs. 1403-1414
• Idioma: inglés
• DOI: 10.4171/RMI/873
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.