Searching for K3 fibrations Original Research Article

We present two methods for studying fibrations of Calabi-Yau manifolds embedded in toric varieties described by single weight systems. We analyze 184 026 such spaces and identify among them the 124 701 which are K3 fibrations. As some of the weights give rise to two or three distinct types of fibrations, the total number we find is 167 406. With our methods one can also study elliptic fibrations of 3-folds and K3 surfaces. We also calculate the Hodge numbers of the 3-folds obtaining more than three times as many as were previously known.