#### Volume 11, issue 1 (2011)

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The Meyer functions for projective varieties and their application to local signatures for fibered $4$–manifolds

### Yusuke Kuno

Algebraic & Geometric Topology 11 (2011) 145–195
##### Abstract

We study a secondary invariant, called the Meyer function, on the fundamental group of the complement of the dual variety of a smooth projective variety. This invariant has played an important role when studying the local signatures of fibered $4$–manifolds from topological point of view. As an application of our study, we define a local signature for generic nonhyperelliptic fibrations of genus $4$ and $5$ and compute some examples.

##### Keywords
mapping class group, Meyer function, bounded cohomology, local signature
##### Mathematical Subject Classification 2000
Primary: 14D05, 57N13
##### Publication
Revised: 2 October 2010
Accepted: 13 October 2010
Published: 6 January 2011
##### Authors
 Yusuke Kuno Department of Mathematics Graduate School of Science Hiroshima University 1-3-1 Kagamiyama Higashi-Hiroshima 739-8526 Japan