# Holonomy representation of quasi-projective leaves of codimension one foliations

## TL;DR

This paper classifies the holonomy representations of quasi-projective leaves in codimension one foliations, showing they are either virtually abelian or factor through an orbicurve after quotienting by their center.

## Contribution

It provides a dichotomy for the structure of holonomy representations of quasi-projective leaves in codimension one foliations, linking them to orbicurves.

## Key findings

- Holonomy representations are either virtually abelian or factor through an orbicurve.
- The structure of these representations is constrained by the geometry of the underlying manifold.
- The results connect foliation theory with orbifold fundamental groups.

## Abstract

We prove that a representation of the fundamental group of a quasi-projective manifold into the group of formal diffeomorphisms of one variable either is virtually abelian or, after taking the quotient by its center, factors through an orbicurve.

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Source: https://tomesphere.com/paper/1704.00484