Vol. 309, No. 2, 2020

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Number of singular fibres of surface fibrations over $\mathbb{P}^1$

Cheng Gong and Yi Gu

Vol. 309 (2020), No. 2, 313–331
Abstract

Let f : X 𝕜1 be a nonisotrivial surface fibration of fibre genus g > 0 over an algebraically closed field 𝕜 of positive characteristic, we study the optimum lower bound for the number of singular fibres of f with respect to the characteristic of 𝕜 in this paper.

Keywords
algebraic surface, singular fibre, positive characteristic
Mathematical Subject Classification 2010
Primary: 14D05, 14D06
Milestones
Received: 21 August 2019
Revised: 16 August 2020
Accepted: 17 November 2020
Published: 14 January 2021
Authors
Cheng Gong
Department of Mathematics
Soochow University
Suzhou
Jiangsu Province
China
Yi Gu
Department of Mathematics
Soochow University
Suzhou
Jiangsu Province
China