Introduction to moduli spaces of instantons on $\mathbf R^4$

In this introductory lecture, I will explain basic properties of moduli spaces of $SU(r)$ -instantons on $\mathbf R^4$ . These spaces can be interpreted as framed moduli spaces of locally free sheaves on the projective plane, and hence have a natural smooth (partial) compactification (by adding non locally free sheaves). These give resolutions of singularities of Uhlenbeck (partial) compactifications. If I have time, I will also introduce quiver varieties as subvarieties of (partial) compactifications.

nakajima@kusm.kyoto-u.ac.jp