On the Reducedness of Quiver Schemes

TL;DR

This paper proves that quiver schemes in characteristic zero are reduced under flat moment maps, and applies this to compute K-theoretic Nekrasov partition functions and characterize flatness for specific quivers.

Contribution

It establishes reducedness of quiver schemes with flat moment maps and connects this to Nekrasov partition functions and W-algebras in type A.

Findings

Reducedness of quiver schemes in characteristic zero with flat moment map

Explicit characterization of flatness for finite and affine type A quivers

Refinement of Losev's theorem relating Nakajima quiver varieties and W-algebras

Abstract

In this paper we prove that a quiver scheme in characteristic zero is reduced if the moment map is flat. We use the reducedness result to show that the equivariant integration formula computes the K-theoretic Nekrasov partition function of five dimensional $\mathcal N=2$ quiver gauge theories when the moment map is flat. We also give an explicit characterization of flatness of moment map for finite and affine type A Dynkin quivers with framings. As an application, we give a refinement of a theorem of Ivan Losev on the relation between quantized Nakajima quiver variety in type A and parabolic finite W-algebra in type A.