Rank-stable limit of completed moduli spaces of instantons

TL;DR

This paper extends Nakajima's resolution of instanton moduli spaces from $S^4$ to $ ext{P}^2$, and computes their homotopy type in the rank-stable limit, revealing universal bundles.

Contribution

It generalizes Nakajima's resolution to $ ext{P}^2$ for ranks up to 4 and determines the homotopy type of the moduli spaces in the rank-stable limit.

Findings

Resolution of singularities extended to $ ext{P}^2$ for $k \\leq 4$

Homotopy type computed in the rank-stable limit

Construction yields universal bundles in the limit

Abstract

Nakajima introduced a resolution of singularities of the Donaldson-Uhlenbeck completion of the moduli space of based instantons over $S^4$. For $k\leq 4$, we extend this result to $\mathbb P^2$ and compute, in the rank-stable limit, the homotopy type of these spaces by showing that, in this limit, these constructions yield universal bundles.