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

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arxiv 2005.12253 v4 pith:X376LMKM submitted 2020-05-25 math.AG

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classification math.AG
keywords pairsabundantscalingamplecanonicalcontainsdiscussdivisor
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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.

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  1. Discreteness of volumes of divisors on Calabi-Yau type varieties

    math.AG 2025-08 conditional novelty 7.0 of 10

    Volumes of integral divisors on epsilon-lc Calabi-Yau pairs lie in a fixed discrete set, settling Birkar's boundedness conjecture for polarized log Calabi-Yau pairs.

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