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arXiv · 1211.1931

Modular Subgroups, Dessins d'Enfants and Elliptic K3 Surfaces

Yang-Hui He·John McKay·James Read
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Abstract

We consider the 33 conjugacy classes of genus zero, torsion-free modular subgroups, computing ramification data and Grothendieck's dessins d'enfants. In the particular case of the index 36 subgroups, the corresponding Calabi-Yau threefolds are identified, in analogy with the index 24 cases being associated with K3 surfaces. In a parallel vein, we study the 112 semi-stable elliptic fibrations over P^1 as extremal K3 surfaces with six singular fibres. In each case, a representative of the corresponding class of subgroups is identified by specifying a generating set for that representative.

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Yang-Hui He, John McKay, James Read. 2012-11-08. Modular Subgroups, Dessins d'Enfants and Elliptic K3 Surfaces. https://doi.org/10.1112/s1461157013000119

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