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.

arXiv comment47 pages, v4:An explanation was added in Theorem 1.7, proof of Lemma 2.11 was improved, other minor changes

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Cited by in corpus (3)

• On the existence of minimal models for log canonical pairs
• Abundance for uniruled pairs which are not rationally connected
• On Nonvanishing for uniruled log canonical pairs