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Existence of log canonical modifications and its applications

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arxiv 2103.01417 v2 pith:2QICGT3J submitted 2021-03-02 math.AG

Osamu Fujino , Kenta Hashizume This is my paper · ORCID
classification math.AG
keywords canonicalexistencemodificationspairsapplicationsestablishsomeadjunction
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The main purpose of this paper is to establish some useful partial resolutions of singularities for pairs from the minimal model theoretic viewpoint. We first establish the existence of log canonical modifications of normal pairs under some suitable assumptions. It recovers Kawakita's inversion of adjunction on log canonicity in full generality. We also discuss the existence of semi-log canonical modifications for demi-normal pairs and construct dlt blow-ups with several extra good properties. As applications, we study lengths of extremal rational curves and so on.

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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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