# Characteristic varieties of graph manifolds and quasi-projectivity of fundamental groups of algebraic links

## TL;DR

This paper investigates the characteristic varieties of graph manifold groups and provides a straightforward proof characterizing algebraic links with quasi-projective fundamental groups, highlighting obstructions to quasi-projectivity.

## Contribution

It offers a new, simplified proof for the characterization of algebraic links with quasi-projective fundamental groups based on characteristic varieties.

## Key findings

- Characteristic varieties of graph manifold groups are analyzed.
- A simple proof characterizing algebraic links with quasi-projective groups is provided.
- Obstructions to quasi-projectivity are identified in the spirit of Papadima's work.

## Abstract

The present paper studies the structure of characteristic varieties of fundamental groups of graph manifolds. As a consequence, a simple proof of Papadima's question is provided on the characterization of algebraic links that have quasi-projective fundamental groups. The type of quasi-projective obstructions used here are in the spirit of Papadima's original work.