Sung Wook Jang, Potential Log Discrepancy and Minimal Model Program III

We can run an MMP for an lc pair. However, in general, we do not know whether the MMP terminates or not. Nevertheless, we can show that special MMP terminates. Immediately, we can prove the existence of minimal models for certain pairs. Analogously, for an anticanonical divisor, if we impose appropriate conditions, then we can say that there exists an anticanonical minimal model. Furthermore, we will talk about ongoing project on anticanonical minimal model program.