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arXiv · 1505.03904

Fibers of Cyclic Covering Fibrations of a Ruled Surface

Makoto Enokizono
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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.

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Makoto Enokizono. 2015-05-14. Fibers of Cyclic Covering Fibrations of a Ruled Surface. https://arxiv.org/abs/1505.03904

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