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


Authors: András I. Stipsicz and Ki-Heon Yun
Journal: Proc. Amer. Math. Soc. 145 (2017), 3607-3616
MSC (2010): Primary 57N13, 53D35
DOI: https://doi.org/10.1090/proc/13480
Published electronically: January 27, 2017
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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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Additional Information

András I. Stipsicz
Affiliation: MTA, Rényi institute of Mathematics, Budapest, Hungary
Email: stipsicz.andras@renyi.mta.hu

Ki-Heon Yun
Affiliation: Department of mathematics, Sungshin Women’s University, Seoul 02844, Korea
Email: kyun@sungshin.ac.kr

DOI: https://doi.org/10.1090/proc/13480
Keywords: Lefschetz fibration, mapping class group
Received by editor(s): June 3, 2016
Received by editor(s) in revised form: September 13, 2016, and September 14, 2016
Published electronically: January 27, 2017
Additional Notes: The authors would like to thank the referee for many valuable comments and F. Catanese for pointing out an error in an earlier version of this paper. The first author was partially supported by ERC Advanced Grant LDTBud and by the Momentum program of the Hungarian Academy of Sciences. The second author was partially supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1D1A1A01058941) and by Sungshin Women’s University study abroad program.
Communicated by: David Futer
Article copyright: © Copyright 2017 American Mathematical Society