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Boundedness in general type MMP and fivefold effective termination (2506.20183v1)
Published 25 Jun 2025 in math.AG
Abstract: 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. As an application, we prove the effective termination of general type MMPs in dimension at most $5$. A key ingredient in the proof is an analysis of the behavior of local volumes in the MMP.
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