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On the Canonical Bundle Formula and Adjunction for Generalized Kaehler Pairs

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arxiv 2404.12007 v1 pith:7F4H2MGW submitted 2024-04-18 math.AG math.CV

Christopher Hacon , Mihai Paun This is my paper · ORCID
classification math.AGmath.CV
keywords generalizedkaehleradjunctionbundlecanonicalformulakawamatapairs
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In this article we prove analogs of Kawamata's canonical bundle formula, Kawamata subadjunction and plt/lc inversion of adjunction for generalized pairs on Kaehler varieties. We also show that a conjecture of BDPPin dimension n-1 implies that the cone theorem holds for any n-dimensional Kaehler generalized klt pair. Along the way, we obtain more complete versions of some results due to Collins-Tosatti and Cao-Hoering.

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Cited by 7 Pith papers

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

  1. A characterization of uniruled compact K\"ahler manifolds

    math.AG 2025-01 accept novelty 8.0 of 10

    A compact Kähler manifold is uniruled exactly when its canonical line bundle is not pseudoeffective, proved by carrying Bost's algebraicity criterion to the Kähler setting.

  2. On the K\"ahler MMP and the transcendental base-point-free theorem

    math.AG 2026-07 accept novelty 7.0 of 10

    Big gklt Kähler pairs admit a full MMP with scaling, and a nef canonical class with modified-big boundary is semiample (Tosatti’s conjecture).

  3. The Miyaoka-Yau inequality for singular varieties with big canonical or anticanonical divisors

    math.AG 2025-07 conditional novelty 7.0 of 10

    For projective klt varieties with big canonical or anticanonical divisor, the Miyaoka-Yau Chern class inequality holds when intersections are taken with the non-pluripolar product.

  4. $P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs

    math.AG 2025-01 conditional novelty 7.0 of 10

    A P-trivial MMP is introduced and used to show that several classes of generalised klt and lc pairs with Nakayama-Zariski decompositions have minimal models.

  5. Transcendental Minimal Model Program for Projective Varieties

    math.AG 2024-12 conditional novelty 7.0 of 10

    For projective generalized klt pairs with a big divisor-plus-transcendental-form boundary, the paper establishes existence of a good minimal model or Mori fiber space, proving Tosatti's conjecture in the projective case.

  6. Remarks on Relative Canonical Bundles and Algebraicity Criteria for Foliations in K\"ahler context

    math.CV 2025-02 conditional novelty 6.0 of 10

    New pseudo-effectivity theorems for relative canonical bundles and new algebraicity and uniruledness criteria for foliations on compact Kähler manifolds are established.

  7. Slope Stable Sheaves and Hermitian-Einstein Metrics on Normal Varieties with Big Cohomology Classes

    math.AG 2025-01 conditional novelty 6.0 of 10

    Slope stability of reflexive sheaves with respect to big classes is equivalent to existence of T-Hermitian-Einstein metrics when the big class has a birational Zariski decomposition with semiample positive part.

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