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K\"ahler-Ricci Tangent Flows are Infinitesimally Algebraic

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arxiv 2312.06577 v2 pith:R22VUMU5 submitted 2023-12-11 math.DG

Max Hallgren This is my paper · ORCID
classification math.DG
keywords ahler-riccialgebraictangentconeregularsenseshrinkingsingular
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abstract

We show that any tangent cone of a singular shrinking K\"ahler-Ricci soliton is a normal affine algebraic variety. Moreover, the regular set of such a tangent cone in the metric sense coincides with the regular set in the algebraic sense. Along the way, we give a parabolic proof of H\"ormander's $L^{2}$ estimate, which can be used to solve the $\overline{\partial}$-equation on any singular shrinking K\"ahler-Ricci soliton.

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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. Remarks on Singular K\"ahler-Einstein Metrics

    math.DG 2025-05 accept novelty 8.0 of 10

    Rough singular Kähler-Einstein metrics, when the metric completion is an RCD space, are equivalent to the Eyssidieux-Guedj-Zeriahi notion and imply log terminal singularities; this applies to tangent cones of noncolla...

  2. Compactness and Rigidity of Complete K\"ahler Ricci Shrinkers

    math.DG 2026-08 conditional novelty 6.0 of 10

    A new first-order visibility argument derives compactness, splitting, and Gaussian rigidity for complete Kähler-Ricci shrinkers from the weight structure of their polarized Fano fibrations.

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