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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Holonomies and the slope inequality of Lefschetz fibrations


Authors: Hideki Miyachi and Hiroshige Shiga
Journal: Proc. Amer. Math. Soc. 139 (2011), 1299-1307
MSC (2010): Primary 14D05; Secondary 30F60, 57M60
Published electronically: October 4, 2010
MathSciNet review: 2748423
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Abstract: In this paper, we consider two necessary conditions: the irreducibility of the holonomy group and the slope inequality for which a Lefschetz fibration over a closed orientable surface is a holomorphic fibration. We show that these two conditions are independent in the sense that neither one implies the other.


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Additional Information

Hideki Miyachi
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka, 560-0043, Japan
Email: miyachi@math.sci.osaka-u.ac.jp

Hiroshige Shiga
Affiliation: Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan
Email: shiga@math.titech.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10563-4
PII: S 0002-9939(2010)10563-4
Keywords: Teichmüller theory, Lefschetz fibration, monodromy, mapping class group, slope inequality
Received by editor(s): July 27, 2009
Received by editor(s) in revised form: April 4, 2010, and April 30, 2010
Published electronically: October 4, 2010
Additional Notes: The first author is partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 21540177, 2009–2013
The second author is partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B), 22340028, 2010–2014.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2010 American Mathematical Society