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Analytic K-semistability and local wall-crossing

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arxiv 2212.08383 v3 pith:5UKQRBCF submitted 2022-12-16 math.DG math.AG

Lars Martin Sektnan , Carl Tipler This is my paper · ORCID
classification math.DGmath.AG
keywords ahlerconstantcsckcurvaturek-polystabilitylocalscalarwall-crossing
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For a small polarised deformation of a constant scalar curvature K\"ahler manifold, under some cohomological vanishing conditions, we prove that K-polystability along nearby polarisations implies the existence of a constant scalar curvature K\"ahler metric. In this setting, we reduce K-polystability to the computation of the classical Futaki invariant on the cscK degeneration. Our result holds on specific families and provides local wall-crossing phenomena for the moduli of cscK manifolds when the polarisation varies.

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Cited by 1 Pith paper

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

  1. Perturbations of Vector Bundle whose Curvature Form Solves a Polynomial Equation

    math.DG 2025-07 conditional novelty 8.0 of 10

    Local existence of solutions to polynomial curvature equations is equivalent to local polystability, with local filtrations and a Kempf-Ness homeomorphism.

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