Chow Rings of Fine Quiver Moduli are Tautologically Presented

TL;DR

This paper demonstrates that the Chow rings of fine quiver moduli spaces are generated by universal bundle Chern classes with relations arising from degeneracy loci, providing a geometric perspective on their structure.

Contribution

It introduces a geometric description of the relations in the Chow ring of fine quiver moduli spaces, extending previous algebraic results.

Findings

Chow rings are generated by universal bundle Chern classes

Relations are geometrically realized as degeneracy loci

Provides a new geometric framework for understanding these Chow rings

Abstract

A result of A. King and C. Walter asserts that the Chow ring of a fine quiver moduli space is generated by the Chern classes of universal bundles if the quiver is acyclic. We will show that defining relations between these Chern classes arise geometrically as degeneracy loci associated to the universal representation.