Hypermaps and multiply quasiplatonic Riemann surfaces

Abstract

Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases with isomorphic automorphism groups.

26 pages. Based on a talk given at the workshop `Groups and Languages' in honour of Antonio Machi, at the Universita di Roma `La Sapienza', September 2010