The number of singular fibers in hyperelliptic Lefschetz fibrations
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, vol.72, no.4, pp.1309-1325, 2020 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 72 Issue: 4
- Publication Date: 2020
- Doi Number: 10.2969/jmsj/82988298
- Journal Name: JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Page Numbers: pp.1309-1325
- Keywords: mapping class groups, Lefschetz fibrations, MINIMAL NUMBER
- Middle East Technical University Affiliated: Yes
Abstract
We consider complex surfaces, viewed as smooth 4-dimensional manifolds, that admit hyperelliptic Lefschetz fibrations over the 2-sphere. In this paper, we show that the minimal number of singular fibers of such fibrations is equal to 2g + 4 for even g >= 4. For odd g >= 7, we show that the number is greater than or equal to 2g + 6. Moreover, we discuss the minimal number of singular fibers in all hyperelliptic Lefschetz fibrations over the 2-sphere as well.