Symmetries of quasiplatonic Riemann surfaces

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 $\mathcal S$ (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.

No reviews yet.

No comments yet.