Elliptic fibrations on Kummer surfaces

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On a K3 surface there may exist more than one elliptic fibration. In order to study detailed arithmetic properties, it is very useful to have many elliptic fibra-tions on a given K3 surface. Our objective is to classify all elliptic fibrations on a given K3 surface and describe them as explicitly as possible. We made a significant progress on this problem in the case of Kummer surfaces associated with curves of genus 2. We also ob-tained some interesting results on K3 surfaces related to modular elliptic surfaces.