Monodromy of elliptic surfaces
نویسندگان
چکیده
grows exponentially. Thus, monodromy groups of elliptic fibrations over P constitute a small, but still very significant fraction of all subgroups of finite index in SL(2,Z). Our goal is to introduce some structure on the set of monodromy groups of elliptic fibrations which would help to answer some natural questions. For example, we show how to describe the set of groups corresponding to rational or K3 elliptic surfaces, explain how to compute the dimensions of the spaces of moduli of surfaces in this class with given monodromy group etc. Our method is based on a detailed study of triangulations of Riemann surfaces. To determine Γ̃ we first describe all possible groups Γ. In order to classify possible Γ we consider the corresponding oriented Riemann surface MΓ. The
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