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<p>For a small polarised deformation of a constant scalar curvature Kähler manifold, under some cohomological vanishing conditions, we prove that <i>K</i>-polystability along nearby polarisations implies the existence of a constant scalar curvature Kähler metric. In this setting, we reduce <i>K</i>-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.</p>

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Analytic K-semistability and local wall-crossing

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月15日

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  • Lars Martin Sektnan,
  • Carl Tipler

摘要

For a small polarised deformation of a constant scalar curvature Kähler manifold, under some cohomological vanishing conditions, we prove that K-polystability along nearby polarisations implies the existence of a constant scalar curvature Kähler 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.