Mordell-Weil lattices of elliptic K3 surfaces

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A K3 surface can have many different elliptic fibrations. Our objective is to classify all elliptic fibrations on a given K3 surface, and describe their Mordell-Weil lattices explicitly. Our principal result was the explicit description of the generators of the Mordell-Weil group of the elliptic fibration of rank 16 to 18 obtained from the Inose fibration on a Kummer surface of product type. This result was made possible through a series of discussions with Prof. Abhinav Kumar of MIT held in the U.S. and Japan during the period between 2012 and 2013.