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Double Kodaira fibrations with small signature

Ju A Lee

Department of Mathematial Sciences, Seoul National University, Seoul 151-747, Korea

E-mail Address: jualee@snu.ac.kr

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Michael Lönne

Mathematik VIII, Universität Bayreuth, Universitätstrasse 30, 95447 Bayreuth, Germany

E-mail Address: michael.loenne@uni-bayreuth.de

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, and

Sönke Rollenske

FB 12/Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Str. 6, 35032 Marburg, Germany

E-mail Address: rollenske@mathematik.uni-marburg.de

Corresponding author.

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https://doi.org/10.1142/S0129167X20500524Cited by:8 (Source: Crossref)

Abstract

Kodaira fibrations are surfaces of general type with a non-isotrivial fibration, which are differentiable fiber bundles. They are known to have positive signature divisible by $4$ . Examples are known only with signature 16 and more. We review approaches to construct examples of low signature which admit two independent fibrations. Special attention is paid to ramified covers of product of curves which we analyze by studying the monodromy action for bundles of punctured curves. As a by-product, we obtain a classification of all fix-point-free automorphisms on curves of genus at most $9$ .

Dedicated to Fabrizio Catanese on the occasion of his 70th birthday.

Keywords:

AMSC: 57R22, 14J29, 14D05

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