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Generalised pairs in birational geometry

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arxiv 2008.01008 v2 pith:YERPSGOY submitted 2020-08-03 math.AG

Caucher Birkar This is my paper · ORCID
classification math.AG
keywords generalisedpairsbirationalgeometryalgebraicapplicationsdescribeevolution
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In this note we introduce generalised pairs from the perspective of the evolution of the notion of space in birational algebraic geometry. We describe some applications of generalised pairs in recent years and then mention a few open problems.

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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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