Lectures on Dessins d'Enfants

“Jarden’s Property and Hurwitz Curves” by Robert A. Kucharczyk

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Robert A. Kucharczyk has a new paper on the ArXiv entitled “Jarden’s Property and Hurwitz Curves”.

Abstract.The purpose of this article is twofold. Firstly we show that the action of the absolute Galois group on certain classes of algebraic curves (Hurwitz curves, Hurwitz translation surfaces) and dessins d’enfants (regular dessins, classical and higher, with fixed signature) is faithful. Secondly we introduce a property of profinite groups, called Jarden’s property, and show this property for certain \’etale fundamental groups. Combining the latter result with faithfulness of the Galois action on these groups, which was known before, we obtain the results on curves and dessins.

You can download the paper here.

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