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

András I. Stipsicz; Ki-Heon Yun

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arXiv · 1604.04877

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

András I. Stipsicz·Ki-Heon Yun

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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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BibTeX RIS

András I. Stipsicz, Ki-Heon Yun. 2016-06-04. On the minimal number of singular fibers in Lefschetz fibrations over the torus. https://arxiv.org/abs/1604.04877

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