On the fundamental groups of effective compact K\"ahler orbifolds with nef anticanonical bundle

TL;DR

This paper proves that the orbifold fundamental group of an effective compact Kähler orbifold with nef anticanonical bundle exhibits polynomial growth, extending previous results from manifolds to orbifolds.

Contribution

It generalizes M.P. Paun's results on fundamental groups from manifolds to orbifolds with nef anticanonical bundles.

Findings

Orbifold fundamental group has polynomial growth.

Extension of manifold results to orbifolds.

Supports conjectures relating curvature and fundamental group growth.

Abstract

We show that the orbifold fundamental group of an effective compact K{\"a}hler orbifold with nef anticanonical bundle has polynomial growth, which generalizes M.P \u{a}un's results for manifolds [P \u{a}u97, Theorem 1,Theorem 2]