ON THE MINIMAL NUMBER OF SINGULAR FIBERS IN LEFSCHETZ FIBRATIONS OVER THE TORUS

摘要

We show that the minimal number of singular fibers N(g, 1) in a genus-g Lefschetz fibration over the torus is at least 3. As an application, we show that N(g, 1) is an element of{3, 4} for g >= 5, N(g, 1) is an element of{3, 4, 5} for g = 3,4 and N(2, 1) = 7.