Orbifold Quot schemes via the Le Bruyn-Procesi theorem

TL;DR

This paper proves that orbifold Quot schemes related to finite subgroups of SL(2,C) are isomorphic to Nakajima quiver varieties, simplifying previous combinatorial and recollement-based proofs.

Contribution

It provides a new, streamlined proof of the isomorphism between orbifold Quot schemes and Nakajima quiver varieties using recent work, avoiding complex combinatorial arguments.

Findings

Reduced orbifold Quot schemes are isomorphic to Nakajima quiver varieties.

The proof bypasses combinatorial and recollement techniques.

Simplifies understanding of the geometric structure of orbifold Quot schemes.

Abstract

This note provides a short proof of the fact that the reduced scheme underlying each orbifold Quot scheme associated to a finite subgroup of SL(2,C) is isomorphic to a Nakajima quiver variety. Our approach uses recent work of the author with Yamagishi, allowing us to bypass the combinatorial arguments and the use of recollement from the original paper with Gammelgaard, Gyenge and Szendroi.