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Erratum and addendum to the paper: Abundance for K\"ahler threefolds

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arxiv 2304.10161 v1 pith:Q55ZGIBI submitted 2023-04-20 math.AG math.CV

Frédéric Campana , Andreas Höring , Thomas Peternell This is my paper · ORCID
classification math.AGmath.CV
keywords ahlercasemaintheoremvalidabundanceaddendumadmit
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In this text we signal a serious gap in the proof of the main theorem of our paper and explain which parts of the statement remain valid. In fact, the main theorem remains valid unless possibly the variety does not admit positive-dimensional subvarieties through a very general point and is not bimeromorphic to a quotient of a torus. This latter case would be ruled out by a Chern class inequality which holds in the algebraic case but is still unknown in the K\"ahler setting.

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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. Holomorphic 1-forms without zeros on K\"ahler threefolds

    math.AG 2025-06 conditional novelty 8.0 of 10

    Every compact Kähler threefold satisfying condition (C) admits a finite étale cover bimeromorphic to a fiber bundle over a torus fiber bundle, yielding a nowhere-vanishing holomorphic 1-form.

  2. Classification of Smooth Minimal K\"ahler Fourfolds Without Effective Divisors and Surfaces

    math.AG 2026-07 conditional novelty 7.0 of 10

    Compact Kähler fourfolds with pseudo-effective K_X and no codimension-1 or -2 subvarieties have torsion K_X, hence are torus quotients or IHS manifolds.

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