# On compact K\"ahler orbifold

## TL;DR

This paper investigates compact Kähler orbifolds, establishing their fundamental properties, regularization techniques, and positivity of orbifold vector bundles, along with an equivariant GAGA version.

## Contribution

It introduces equivalence of notions for compact Kähler orbifolds, extends Demailly's regularization to orbifolds, and discusses orbifold vector bundle positivity and equivariant GAGA.

## Key findings

- Proves the equivalence of two definitions of compact Kähler orbifolds.
- Extends Demailly's regularization theorems to orbifolds.
- Provides a version of equivariant GAGA for orbifolds.

## Abstract

In this paper, we study compact complex orbifolds. In the first part, we shows the equivalence of two notions of compact K\"ahler orbifold. In the second part, we shows various versions of Demailly's regularisation theorems for compact orbifold and study the positivity of orbifold vector bundle. In the last section, we give a version of equivariant GAGA communicated to us by Brion.