Unitary representations of the fundamental group of Orbifolds

TL;DR

This paper extends the known correspondence between polystable vector bundles and unitary representations from smooth varieties to smooth orbifolds, broadening the scope of this fundamental relationship.

Contribution

It generalizes the bijective correspondence to include smooth orbifolds, a significant extension of the classical theory.

Findings

The correspondence holds for smooth orbifolds.

Polystable vector bundles with trivial Chern classes correspond to unitary representations.

The extension preserves the bijective nature of the classical correspondence.

Abstract

There is a well known bijective correspondence between isomorphism classes of polystable vector bundles $E$ with $c_i(E)=0$ for $i\geq 1$ on a smooth complex projective variety and equivalence classes of unitary representations of the fundamental group of the variety. We show that this bijective correspondence extends to smooth orbifolds.