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

Stipsicz, András and Ki-Heon, Yun (2017) On the minimal number of singular fibers in Lefschetz fibrations over the torus. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 145 (8). pp. 3607-3616. ISSN 0002-9939

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

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