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Nakajima introduced a resolution of singularities of the Donaldson-Uhlenbeckcompletion 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, theseconstructions yield universal bundles.

Rank-stable limit of completed moduli spaces of instantons