## Tohoku Mathematical Journal

- Tohoku Math. J. (2)
- Volume 71, Number 3 (2019), 327-358.

### Fibers of cyclic covering fibrations of a ruled surface

#### Abstract

We give an algorithm to classify singular fibers of finite cyclic covering fibrations of a ruled surface by using singularity diagrams. As the first application, we classify all fibers of 3-cyclic covering fibrations of genus 4 of a ruled surface and show that the signature of a complex surface with this fibration is non-positive by computing the local signature for any fiber. As the second application, we classify all fibers of hyperelliptic fibrations of genus 3 into 12 types according to the Horikawa index. We also prove that finite cyclic covering fibrations of a ruled surface have no multiple fibers if the degree of the covering is greater than 3.

#### Article information

**Source**

Tohoku Math. J. (2), Volume 71, Number 3 (2019), 327-358.

**Dates**

First available in Project Euclid: 18 September 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.tmj/1568772176

**Digital Object Identifier**

doi:10.2748/tmj/1568772176

**Mathematical Reviews number (MathSciNet)**

MR4012353

**Subjects**

Primary: 14D06: Fibrations, degenerations

**Keywords**

fibered surface singular fiber cyclic covering

#### Citation

Enokizono, Makoto. Fibers of cyclic covering fibrations of a ruled surface. Tohoku Math. J. (2) 71 (2019), no. 3, 327--358. doi:10.2748/tmj/1568772176. https://projecteuclid.org/euclid.tmj/1568772176