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arXiv · 2312.13916

On Elliptic K3 Surfaces and Dessins d'Enfants

Michael Lönne·Matteo Penegini
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Abstract

We classify subgroups of $\textrm{SL}(2,\mathbb{Z})$ up to conjugacy, which occur as monodromy groups of elliptically fibered K3 surfaces following a general strategy proposed by Bogomolov and Tschinkel. The essential step is the factorisation of the functional invariant $j$ with second factor a Belyi function of maximal possible degree and the classification of the corresponding subgroups $\bar\Gamma$ of $\textrm{PSL}(2,\mathbb{Z})$ using dessins d'enfants.

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Michael Lönne, Matteo Penegini. 2023-12-21. On Elliptic K3 Surfaces and Dessins d'Enfants. https://arxiv.org/abs/2312.13916

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