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Log Calabi--Yau pairs of complexity zero and arbitrary index

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arxiv 2411.05343 v1 pith:6TES4E33 submitted 2024-11-08 math.AG

Joshua Enwright , Fernando Figueroa This is my paper · ORCID
classification math.AG
keywords calabi--yaucomplexityzeroarbitrarybirationalindexpairsadmits
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In this article, we give a characterization of log Calabi--Yau pairs of complexity zero and arbitrary index. As an application, we show that a log Calabi--Yau pair of birational complexity zero admits a crepant birational model which is a generalized Bott tower.

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Cited by 2 Pith papers

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  1. Complexity one varieties are cluster type

    math.AG 2025-04 conditional novelty 7.0 of 10

    A log Calabi-Yau pair of index one and complexity at most one is a cluster type variety, and varieties of absolute complexity one admit a finite cluster type cover of degree at most two.

  2. Calabi-Yau pairs of complexity two

    math.AG 2024-12 conditional novelty 7.0 of 10

    A Calabi-Yau pair of complexity two is cluster type exactly when its standard model over a toric base is nodal, component-compatible, and volume-large; this classifies all rank-one Gorenstein del Pezzo surfaces.

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