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

TL;DR

This paper investigates the Meyer function invariant related to projective varieties and applies it to define and compute local signatures for certain fibered 4-manifolds, advancing topological understanding.

Contribution

It introduces a new application of Meyer functions to define local signatures for non-hyperelliptic fibrations of genus 4 and 5, with explicit computations.

Findings

Defined local signatures for specific fibered 4-manifolds

Computed examples illustrating the application of Meyer functions

Enhanced understanding of topological invariants in algebraic geometry

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 have 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 non-hyperelliptic fibrations of genus 4 and 5 and compute some examples.