The number of singular fibers in hyperelliptic Lefschetz fibrations


ALTUNÖZ T.

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, vol.72, no.4, pp.1309-1325, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.2969/jmsj/82988298
  • Title of Journal : JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
  • Page Numbers: pp.1309-1325

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.