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.
Citation
Makoto Enokizono. "Fibers of cyclic covering fibrations of a ruled surface." Tohoku Math. J. (2) 71 (3) 327 - 358, 2019. https://doi.org/10.2748/tmj/1568772176