After giving an overview of derived categories, Minimal Model Program (MMP) in birational geometry and finally Bridgeland stability conditions, I will describe a new wall-crossing phenomenon of sheaves on the projective 3-space that induces singularities which are not mild enough in the sense of the Minimal Model Program. Therefore, the wall-crossing cannot be understood as an operation in the MMP of the moduli space, unlike the case for many surfaces.