Analytic K-semistability and local wall-crossing

Lars Martin Sektnan; Carl Tipler

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arXiv · 2212.08383

Analytic K-semistability and local wall-crossing

Lars Martin Sektnan·Carl Tipler

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Abstract

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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Lars Martin Sektnan, Carl Tipler. 2022-12-16. Analytic K-semistability and local wall-crossing. https://arxiv.org/abs/2212.08383

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