The number of singular fibers in hyperelliptic Lefschetz fibrations


ALTUNÖZ T.

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, cilt.72, ss.1309-1325, 2020 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 72 Konu: 4
  • Basım Tarihi: 2020
  • Doi Numarası: 10.2969/jmsj/82988298
  • Dergi Adı: JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
  • Sayfa Sayıları: ss.1309-1325

Özet

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.