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Singular K\"ahler-Einstein metrics and RCD spaces

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arxiv 2408.10747 v2 pith:C3G7TMA3 submitted 2024-08-20 math.DG

Gábor Székelyhidi This is my paper · ORCID
classification math.DG
keywords metricsahler-einsteinsingularapproximationcompletionconstantcurvaturehomeomorphic
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We study K\"ahler-Einstein metrics on singular projective varieties. We show that under an approximation property with constant scalar curvature metrics, the metric completion of the smooth part is a non-collapsed RCD space, and is homeomorphic to the original variety.

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Cited by 6 Pith papers

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

  1. H\"older estimates for degenerate complex Monge-Amp\`ere equations

    math.CV 2025-08 conditional novelty 8.0 of 10

    Hölder estimates for degenerate complex Monge-Ampère equations are established on smoothable singular Kähler varieties, confirming a conjecture for Kähler-Einstein potentials.

  2. Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations

    math.DG 2025-05 accept novelty 8.0 of 10

    The Gromov-Hausdorff limit of collapsing Calabi-Yau metrics is homeomorphic to the base variety, and the singular set has Hausdorff codimension at least two.

  3. On K\"ahler-Einstein Currents

    math.DG 2025-02 conditional novelty 8.0 of 10

    Singular Kähler-Einstein metrics on klt pairs define Kähler currents, and a tame approximation with L^p Ricci control suffices to make the metric completion an RCD space.

  4. Nash entropy, Calabi energy and geometric regularization of singular K\"ahler metrics

    math.DG 2025-02 conditional novelty 8.0 of 10

    Singular Kähler metrics with Ricci curvature bounded below and rational cohomology class induce non-collapsed RCD spaces homeomorphic to the projective variety, under a resolution condition on the anti-canonical bundle.

  5. Uniform estimates: from Yau to Kolodziej

    math.DG 2025-02 accept novelty 6.0 of 10

    A new envelope-based reduction proves uniform a priori estimates from Yau's L^p bound, recovering and extending Kolodziej's Orlicz-type criterion.

  6. Ricci-flat metrics on Calabi-Yau manifolds

    math.DG 2025-09 unverdicted novelty 2.0 of 10

    A survey of the degeneration theory of Ricci-flat Kahler metrics on Calabi-Yau manifolds: smooth limits for semiample and nef-and-big classes, path-dependent counterexamples at the boundary, and a list of open conjectures.

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