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.

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.