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arXiv · 2505.10828

K-polystability and reduced uniform K-stability of log Fano cone singularities

Linsheng Wang
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Abstract

We prove that a log Fano cone $(X,\Delta,\xi_0)$ satisfying $\delta_\mathbb{T}(X,\Delta,\xi_0)\ge 1$ is K-polystable for normal test configurations if and only if it is K-polystable for special test configurations. We also establish the reduced uniform K-stability of $(X,\Delta,\xi_0)$ and show that it is equivalent to K-polystability.

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Linsheng Wang. 2025-05-16. K-polystability and reduced uniform K-stability of log Fano cone singularities. https://arxiv.org/abs/2505.10828

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