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Modular Subgroups, Dessins d’Enfants and Elliptic K3 Surfaces

He, Y., McKay, J.M. and Read, J. (2013). Modular Subgroups, Dessins d’Enfants and Elliptic K3 Surfaces. LMS Journal of Computation and Mathematics, 16, pp. 271-318. doi: 10.1112/S1461157013000119

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 to K3 surfaces. In a parallel vein, we study the 112 semi-stable elliptic fibrations over P1 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.

Publication Type: Article
Additional Information: Copyright Cambridge Journals, 2013. Content and layout follow Cambridge University Press’s submission requirements. This version may have been revised following peer review but may be subject to further editorial input by Cambridge University Press.
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/12867
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