Finiteness of log Abundant log Canonical Pairs in log Minimal Model Program with Scaling

Abstract

We study relations between property of being log abundant for lc pairs and termination of log MMP with scaling. We prove that any log MMP with scaling of an ample divisor starting with a projective dlt pair contains only finitely many log abundant dlt pairs. In addition, we discuss conjectures on log abundant dlt pairs which imply existence of good minimal models for projective klt pairs.