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

Cheng Gong and Yi Gu

Vol. 309 (2020), No. 2, 313–331

DOI: 10.2140/pjm.2020.309.313

Abstract

Let $f:X\to {\mathbb{P}}_{\mathbb{𝕜}}^1$ be a nonisotrivial surface fibration of fibre genus $g>0$ over an algebraically closed field $\mathbb{𝕜}$ of positive characteristic, we study the optimum lower bound for the number of singular fibres of $f$ with respect to the characteristic of $\mathbb{𝕜}$ 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