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

2016/04/17 by Stipsicz, András I., Yun, Ki-Heon
#53D35 #57N13 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1604.04877

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.

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