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arXiv · 1401.2575

Symmetries of quasiplatonic Riemann surfaces

Gareth A. Jones·David Singerman·Paul D. Watson
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Abstract

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.

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Gareth A. Jones, David Singerman, Paul D. Watson. 2014-01-11. Symmetries of quasiplatonic Riemann surfaces. https://arxiv.org/abs/1401.2575

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