On minimal model theory for log abundant lc pairs

Abstract

Under the assumption of the minimal model theory for projective klt pairs of dimension $n$, we establish the minimal model theory for lc pairs $(X/Z,\Delta )$ such that the log canonical divisor is relatively log abundant and its restriction to any lc center has relative numerical dimension at most $n$. We also give another detailed proof of results by the second author, and study termination of log MMP with scaling.

47 pages, v4:An explanation was added in Theorem 1.7, proof of Lemma 2.11 was improved, other minor changes