Generalised Fermat Hypermaps and Galois Orbits

Abstract

We consider families of quasiplatonic Riemann surfaces characterised by the fact that — as in the case of Fermat curves of exponent n — their underlying regular (Walsh) hypermap is an embedding of the complete bipartite graph Kn,n , where n is an odd prime power. We show that these surfaces, regarded as algebraic curves, are all defined over abelian number… (More)

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