# Slope inequalities for irregular cyclic covering fibrations

## TL;DR

This paper investigates the lower bounds of the slope for cyclic covering fibrations of fibered surfaces, especially when the relative irregularity is positive, contributing to the understanding of geometric inequalities.

## Contribution

It provides new slope inequalities for irregular cyclic covering fibrations, extending previous results to cases with positive relative irregularity.

## Key findings

- Established lower bounds for the slope in irregular cases
- Extended slope inequality theory to cyclic coverings with positive irregularity
- Enhanced understanding of the geometry of fibered surfaces

## Abstract

Let $f:S\to B$ be a finite cyclic covering fibration of a fibered surface. We study the lower bound of slope $\lambda_{f}$ when the relative irregularity $q_{f}$ is positive.