Moduli spaces of framed perverse instantons on $\mathbb P^3$

I will talk about moduli spaces of framed perverse instantons on $\mathbb P^3$. As an open subset they contain the moduli space of framed instantons studied by I. Frenkel and M. Jardim. I will explain the connection with the moduli space of pairs on the blow up of $\mathbb P^3$ along a line. I will also study the map between the Gieseker and Donaldson-Uhlenbeck partial compactifications of the moduli space of instantons on $\mathbb P^3$. Finally I will construct a few counterexamples to earlier conjectures and results concerning these moduli spaces.