A noncommutative-geometric interpretation of the resolution of equivariant instanton moduli spaces

Abstract

We generalize the recently proposed noncommutative ADHM construction to the case of $\Gamma$-equivariant instantons over $\R^4$, with $\Gamma$ a Kleinian group. We show that a certain form of the inhomogeneous ADHM equations describes instantons over a noncommutative deformation of the Kleinian orbifold $\C^2/\Gamma$ and we discuss the relation of this with Nakajima's description of instantons over ALE spaces. In particular, we obtain a noncommutative interpretation of the minimal resolution of Kleinian singularities.