Families of curves over [formula omitted] with 3 singular fibers

Abstract

Suppose f:S→P1 is a fibration of genus g with 3 singular fibers and two of them are semistable. We show that the Mordell–Weil group of f is finite, the surface S is rational and 2g⩽−KS2⩽4g−4. We construct some examples to show that such fibrations exist for infinitely many g.