Kodaira dimension of Lefschetz fibrations over tori
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- by Josef G. Dorfmeister PDF
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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.References
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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
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1711-1716
- MSC (2010): Primary 53D35, 57R17
- DOI: https://doi.org/10.1090/proc/12797
- MathSciNet review: 3451246