Asian Journal of Mathematics

Volume 21 (2017)

Number 5

On lower bounds for slopes of totally ramified triple cover fibrations

Pages: 981 – 994

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

Authors

Pan Liu (Department of Mathematics, and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, China)

Jun Lu (Department of Mathematics, and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, China)

Fei Ye (Department of Mathematics and Computer Science, Queensborough Community College CUNY, New York, N.Y., U.S.A.)

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

Full Text (PDF format)

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