Quiver varieties and framed sheaves on compactified Kleinian singularities.

Consider a Kleinian singularity ℂ2/Γ, where Γ is a finite subgroup of <bold>SL</bold>2(ℂ). In this paper, we introduce a natural stack compactifying the singularity by adding a smooth stacky divisor, and we show that sets of framed sheaves on this stack satisfying certain additional criteria are closely related to a class of Nakajima quiver varieties. This partially extends our previous work on punctual Hilbert schemes of Kleinian singularities. [ABSTRACT FROM AUTHOR]