SEARCHING FOR K3 FIBRATIONS

We present two methods for studying fibrations of Calabi-Yau manifolds embedded in toric varieties described by single weight systems, We an alyze 184026 such spaces and identify among them the 124701 which are K3 fibrations. As some of the weights give rise to two or three distin ct types of fibrations, the total number we find is 167406, With our m ethods one can also study elliptic fibrations of 3-folds and K3 surfac es. We also calculate the Hedge numbers of the 3-folds obtaining more than three times as many as were previously known. (C) 1997 Elsevier S cience B.V.