Tohoku Mathematical Journal
2019
September
SECOND SERIES VOL. 71, NO. 3

Tohoku Math. J.
71 (2019), 327-358

Title FIBERS OF CYCLIC COVERING FIBRATIONS OF A RULED SURFACE

Author Makoto Enokizono

(Received March 18, 2016, revised May 10, 2017)
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.

Mathematics Subject Classification. Primary 14D06.
Key words and phrases. Fibered surface, singular fiber, cyclic covering.

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