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arXiv · 1509.05819

An explicit quasiplatonic curve with non-abelian moduli field

Moisés Herradón Cueto
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Abstract

We give an example of a regular dessin d'enfant whose field of moduli is not an abelian extension of the rational numbers, namely it is the field generated by a cubic root of 2. This answers a previous question. We also prove that the underlying curve has non-abelian field of moduli itself, giving an explicit example of a quasiplatonic curve with non-abelian field of moduli. In the last section, we note that two examples in previous literature can be used to find other examples of regular dessins d'enfants with non-abelian field of moduli.

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Moisés Herradón Cueto. 2016-04-20. An explicit quasiplatonic curve with non-abelian moduli field. https://doi.org/10.1007/s13163-016-0196-z

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