# Introduction to moduli spaces of instantons on

In this introductory lecture, I will explain basic properties of moduli spaces of -instantons on . 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