Asian Journal of Mathematics

Volume 22 (2018)

Number 4

Special issue in honor of Ngaiming Mok (3 of 3)

Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University

Remarks on Xiao’s approach of slope inequalities

Pages: 691 – 704

DOI: https://dx.doi.org/10.4310/AJM.2018.v22.n4.a5

Authors

Hao Sun (Department of Mathematics, Shanghai Normal University, Shanghai, China)

Xiaotao Sun (Center of Applied Mathematics, School of Mathematics, Tianjin University, Tianjin, China)

Mingshuo Zhou (Center of Applied Mathematics, School of Mathematics, Tianjin University, Tianjin, China)

Abstract

We prove the slope inequality for a relative minimal surface fibration in positive characteristic via Xiao’s approach. We also prove a better low bound for the slope of non-hyperelliptic fibrations.

Keywords

slope inequality, surface fibration, non-hyperelliptic fibration, Harder–Narasimhan filtration, strongly semi-stable

2010 Mathematics Subject Classification

14J25, 14Q10

Full Text (PDF format)

Hao Sun is supported by the National Natural Science Foundation of China (No. 11301201).

Xiaotao Sun is supported by the National Natural Science Foundation of China (No. 11321101).

Mingshuo Zhou is supported by the National Natural Science Foundation of China (No. 11501154) and Natural Science Foundation of Zhejiang Provincial (No. LQ16A010005).

Received 11 August 2016

Accepted 2 June 2017

Published 20 September 2018