Finiteness of log abundant log canonical pairs in log minimal model program with scaling

Abstract

We study relations between the property of being log abundant for lc pairs and the 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. We also discuss log MMP for slc pairs.

51 pages. Final version. To appear in Michigan Math. J

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