Almost-Regular Dessins on a Sphere and Torus

Joachim König; Arielle Leitner; Danny Neftin

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arXiv · 1709.06869

Almost-Regular Dessins on a Sphere and Torus

Joachim König·Arielle Leitner·Danny Neftin

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Abstract

The Hurwitz problem asks which ramification data are realizable, that is appear as the ramification type of a covering. We use dessins d'enfant to show that families of genus 1 regular ramification data with small changes are realizable with the exception of four families which were recently shown to be nonrealizable. A similar description holds in the case of genus 0 ramification data.

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Joachim König, Arielle Leitner, Danny Neftin. 2017-09-20. Almost-Regular Dessins on a Sphere and Torus. https://arxiv.org/abs/1709.06869

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