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Kodaira dimension of Lefschetz fibrations over tori


Author: Josef G. Dorfmeister
Journal: Proc. Amer. Math. Soc. 144 (2016), 1711-1716
MSC (2010): Primary 53D35, 57R17
Published electronically: November 4, 2015
MathSciNet review: 3451246
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Abstract: The Kodaira dimension for Lefschetz fibrations was defined in 2009 by Dorfmeister and Zhang. In this note we show that there exists no Lefschetz fibration over a torus with fiber genus $ g\ge 3$ of Kodaira dimension 1. This proves that the Lefschetz Kodaira dimension is a diffeomorphism invariant.


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Additional Information

Josef G. Dorfmeister
Affiliation: Department of Mathematics, North Dakota State University, Fargo, North Dakota 58102
Email: josef.dorfmeister@ndsu.edu

DOI: https://doi.org/10.1090/proc/12797
Received by editor(s): March 23, 2015
Received by editor(s) in revised form: April 2, 2015
Published electronically: November 4, 2015
Additional Notes: The author was partially supported by the Simons Foundation $#$246043.
Communicated by: Martin Scharlemann
Article copyright: © Copyright 2015 American Mathematical Society