Uhlenbeck-Donaldson compactification for framed sheaves

We introduce the moduli spaces of framed sheaves. A reason for being interested in these objects is that under suitable conditions they are nice moduli spaces (quasi-projective, smooth and fine) and provide desingularizations of moduli spaces of framed instantons. We study a “partial compactification” for these moduli spaces, called the Uhlenbeck-Donaldson compactification, and relate it to the moduli space of "ideal" framed instantons.