Minimal number of singular fibers in Lefschetz fibrations over the torus

András I. Stipsicz, Ki-Heon Yun

Published 2016-04-17Version 1

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