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An abundance theorem for generalised pairs

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arxiv 2103.11813 v1 pith:5AGLVVTU submitted 2021-03-22 math.AG

Zhengyu Hu This is my paper · ORCID
classification math.AG
keywords generalisedabundancepairscanonicalprovetheoremabundantconsequence
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abstract

We prove the finiteness of $B$-representations of generalised log canonical pairs. As a consequence, we prove that, the (relative) abundance for a generalised semi-log canonical pair is implied by the abundance for its normalisation. Furthermore, we obtain an abundance theorem for generalised dlt pairs with abundant data, which is a natural inductive step of generalised minimal model program.

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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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