On Elliptic K3 Surfaces and Dessins d'Enfants
Abstract
We classify subgroups of SL(2,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 of PSL(2,Z) using dessins d'enfants.
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