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# Asian Journal of Mathematics

## Volume 21 (2017)

### Number 5

### On lower bounds for slopes of totally ramified triple cover fibrations

Pages: 981 – 994

DOI: https://dx.doi.org/10.4310/AJM.2017.v21.n5.a8

#### Authors

#### Abstract

Let $f : S \to C$ be a totally ramified triple cover fibration of type $(g, \gamma)$. We prove that the slope of $f$ has a sharp lower bound $\frac{24 (g - 1)}{5g - 6 \gamma +1}$ given that $g \gt \frac{15}{2} \gamma + \frac{5}{2}$. We also characterize fibrations that achieve the bound.

#### Keywords

triple cover, slope, index theorem, singularity

#### 2010 Mathematics Subject Classification

13B22, 14F05, 14H30

This work is supported by the NSFC and the Science and Technology Commission of Shanghai Municipality (STCSM), No. 13DZ2260400.

Received 26 April 2015

Accepted 5 May 2016

Published 9 February 2018