On the minimal number of singular fibers in Lefschetz fibrations over the torus

Stipsicz, András; Yun, Ki-Heon

doi:10.1090/proc/13480

On the minimal number of singular fibers in Lefschetz fibrations over the torus
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by András I. Stipsicz and Ki-Heon Yun PDF

Proc. Amer. Math. Soc. 145 (2017), 3607-3616 Request permission

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 $N(g, 1) \in \{ 3, 4\}$ for $g\ge 5$, $N(g, 1) \in \{3, 4,5 \}$ for $g= 3, 4$ and $N(2,1) = 7$.

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