An alternative way to solve the Cohen-Macaulay-ness conjecture in the quiver variety

TL;DR

This paper proposes a novel approach using homological algebra to address the Cohen-Macaulay-ness conjecture in the geometry of quiver varieties, offering an alternative perspective to existing methods.

Contribution

It introduces a new homological algebra-based method to study the Cohen-Macaulay-ness conjecture in quiver varieties, expanding the toolkit for this problem.

Findings

Provides an alternative proof strategy for the conjecture.

Highlights the potential of homological algebra in geometric conjectures.

Suggests new directions for research in quiver variety geometry.

Abstract

This short paper is another way to say that one can attack the Cohen-Macaulay-ness conjecture in the geometry of quiver variety using homological algebra.