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 | References | Similar Articles | Additional Information

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

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