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

Linsheng Wang

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

Algebraic Geometry 2026-03-26 v2

Authors: Linsheng Wang

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.

Keywords

K-polystability uniform K-stability log Fano varieties test configurations cone singularities

Cite

@article{arxiv.2505.10828,
  title  = {K-polystability and reduced uniform K-stability of log Fano cone singularities},
  author = {Linsheng Wang},
  journal= {arXiv preprint arXiv:2505.10828},
  year   = {2026}
}

Comments

39 pages. v2: Section 5 expanded, proof of Theorem 1.4 modified, and an appendix on local Okounkov bodies added

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

Abstract

Keywords

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