Sur l'uniformisation des orbifolds K\"ahl\'eriens compacts

TL;DR

This paper extends uniformisation results from compact K"ahler manifolds to K"ahler orbifolds, addressing conjectures related to their fundamental groups and complex structure.

Contribution

It generalizes key uniformisation theorems to the setting of K"ahler orbifolds, broadening the scope of classical results.

Findings

Extension of uniformisation results to K"ahler orbifolds

Progress on the Shafarevich conjecture for orbifolds

Insights into the structure of orbifold fundamental groups

Abstract

This article generalises to K\"ahler orbifolds general results on uniformisation of compact K\"ahler manifolds such as the Shafarevich conjecture for linear fundamental groups.