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Boundedness in general type MMP

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arxiv 2506.20183 v2 pith:HPJYMIMU submitted 2025-06-25 math.AG

Jingjun Han , Lu Qi , Ziquan Zhuang This is my paper · ORCID
classification math.AG
keywords generaltypeanalysisbehaviorbelongboundedboundednesscontractions
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We show that in any sequence of a general type MMP, the minimal log discrepancy of singularities takes at most finitely many values, and the fibers of all the extremal contractions and flips belong to a bounded family. A key ingredient in the proof is an analysis of the behavior of local volumes in the MMP.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Effective termination of general type MMPs in dimension at most five

    math.AG 2025-09 conditional novelty 8.0 of 10

    Every general type MMP in dimension at most five terminates; explicit step-count bounds are given in dimensions three and four.

  2. 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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