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
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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 $N(2,1) = 7$.References
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Additional Information
- András I. Stipsicz
- Affiliation: MTA, Rényi institute of Mathematics, Budapest, Hungary
- MR Author ID: 346634
- Email: stipsicz.andras@renyi.mta.hu
- Ki-Heon Yun
- Affiliation: Department of mathematics, Sungshin Women’s University, Seoul 02844, Korea
- MR Author ID: 788980
- Email: kyun@sungshin.ac.kr
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3607-3616
- MSC (2010): Primary 57N13, 53D35
- DOI: https://doi.org/10.1090/proc/13480
- MathSciNet review: 3652812