Anticanonical divisor with good asymptotic base loci

In this paper, we give a characterization of Fano type varieties in terms of the asymptotic base loci of $-(K_X+\mathrm{\Delta })$. We also show that for a potentially lc pair $(X,\mathrm{\Delta })$, if no plc centers are contained in the augmented base locus ${\mathbf{B}}_{+}(-(K_X+\mathrm{\Delta }))$, then $(X,\mathrm{\Delta })$ has a good $-(K_X+\mathrm{\Delta })$-minimal model. This gives an analogous result of Birkar–Hu on the existence of good minimal models.