Fibers of cyclic covering fibrations of a ruled surface

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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.

Original languageEnglish
Pages (from-to)327-358
Number of pages32
JournalTohoku Mathematical Journal
Volume71
Issue number3
DOIs
Publication statusPublished - Sep 2019

Keywords

  • Cyclic covering
  • Fibered surface
  • Singular fiber

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