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

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.