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

Kuno, Yusuke

doi:10.2140/agt.2011.11.145

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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

DOI: 10.2140/agt.2011.11.145

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

References

Publication

Received: 6 May 2010

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

Volume 11, issue 1 (2011)