Anticanonical divisor with good asymptotic base loci

Abstract

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