Remarks on Xiao's approach of Slope inequalities

TL;DR

This paper extends Xiao's approach to prove the slope inequality for relative minimal surface fibrations in positive characteristic and improves bounds for non-hyperelliptic cases.

Contribution

It adapts Xiao's method to positive characteristic and establishes a sharper slope bound for non-hyperelliptic fibrations.

Findings

Proved slope inequality for surface fibrations in positive characteristic.

Established a better lower bound for non-hyperelliptic fibrations.

Extended Xiao's approach to new cases.

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.