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On the cone conjecture for certain pairs of dimension at most 4

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arxiv 2405.20899 v2 pith:MG5XFM4C submitted 2024-05-31 math.AG

Fulin Xu This is my paper · ORCID
classification math.AG
keywords coneconjecturedimensionpairsanti-canonicalcalabi-yaucertainconsidering
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abstract

In this paper, by running MMP and considering the anti-canonical fibration, we prove the Morrison-Kawamata cone conjecture for klt Calabi-Yau pairs $(X,\Delta)$ such that $\dim X$ is at most $4$, and the Iitaka dimension $\kappa(X,-K_X)$ is at least $\dim X - 2$.

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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. On the Morrison-Kawamata dream space and its applications

    math.AG 2025-12 conditional novelty 7.0 of 10

    An axiomatic framework (MKD spaces) yields deformation-invariance of divisor cones and a conditional boundedness theorem for rationally connected Calabi–Yau varieties.

  2. On the boundedness of elliptic Calabi-Yau 4-folds

    math.AG 2026-07 accept novelty 6.0 of 10

    Elliptic Calabi–Yau 4-folds not crepant to a product quotient of a Calabi–Yau 3-fold times an elliptic curve form a bounded family.

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