Birational geometry of moduli spaces of perverse coherent sheaves on blow-ups

In order to study wall crossing formula of Donaldson type invariants on the blown-up plane, Nakajima-Yoshioka constructed a sequence blow-up/blow-down diagrams connecting moduli space torsion free framed sheaves projective and that its blow-up. this paper, we prove Nakajima-Yoshioka's diagram realizes minimal model program. Furthermore, obtain fully-faithful embedding between derived categories these spaces.