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 $g\geq4$. For odd $g\geq7$, 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.
The author was partially supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK).
"The number of singular fibers in hyperelliptic Lefschetz fibrations." J. Math. Soc. Japan 72 (4) 1309 - 1325, October, 2020. https://doi.org/10.2969/jmsj/82988298