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Birational complexity and dual complexes

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arxiv 2402.10136 v2 pith:7WKFXI6Z submitted 2024-02-15 math.AG

Mirko Mauri , Joaquín Moraga This is my paper · ORCID
classification math.AG
keywords birationalpaircalabi-yaucomplexescomplexitydualinvariantfocus
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We introduce the notion of birational complexity of a log Calabi-Yau pair. This invariant measures how far the log Calabi-Yau pair is to being birational to a toric pair. We study fundamental properties of the new invariant, with a particular focus on the geometry of dual complexes.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Bott-Chern complexity of K\"ahler pairs

    math.AG 2025-05 accept novelty 7.0 of 10

    The Bott-Chern complexity of a non-projective Calabi-Yau Kähler pair is at least 3, and this bound is attained by singular non-projective K3 surfaces with Picard rank zero.

  2. 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.

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