Minimal number of singular fibers in Lefschetz fibrations over the torus

Abstract

Abstract. 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) ∈ {3, 4} for g ≥ 5, N (g, 1) ∈ {3, 4, 5} for g = 3, 4 and N (2, 1) = 7.