On the connection between affine and projective fundamental groups of line arrangements and curves

TL;DR

This paper explores the relationship between affine and projective fundamental groups of line arrangements and reducible curves, providing a decomposition theorem and applications to better understand their topological properties.

Contribution

It introduces a new decomposition relating affine and projective fundamental groups for line arrangements and reducible curves with a line component.

Findings

Established a decomposition theorem connecting affine and projective fundamental groups.

Applied the decomposition to specific classes of line arrangements and curves.

Enhanced understanding of the topological structure of line arrangements and reducible curves.

Abstract

In this note we prove a decomposition related to the affine fundamental group and the projective fundamental group of a line arrangement and a reducible curve with a line component. We give some applications to this result.