A remark on the Hard Lefschetz Theorem for K\"ahler orbifolds

TL;DR

This paper provides a new proof of the hard Lefschetz theorem for Kähler orbifolds, avoiding intersection homology, and addresses a question posed by Fulton using foliated geometry techniques.

Contribution

It introduces a novel proof method for the hard Lefschetz theorem on orbifolds based on foliated geometry, bypassing intersection homology.

Findings

Proof of the hard Lefschetz theorem for orbifolds without intersection homology

Answers Fulton's question on orbifold cohomology

Utilizes foliated version of the theorem by El Kacimi

Abstract

We give a proof of the hard Lefschetz theorem for orbifolds that does not involve intersection homology. This answers a question of Fulton. We use a foliated version of the hard Lefschetz theorem due to El Kacimi.