K-polystability and reduced uniform K-stability of log Fano cone singularities
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914420750286848 |
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| author | Wang, Linsheng |
| author_facet | Wang, Linsheng |
| contents | We prove that a log Fano cone $(X,Δ,ξ_0)$ satisfying $δ_\mathbb{T}(X,Δ,ξ_0)\ge 1$ 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 $(X,Δ,ξ_0)$ and show that it is equivalent to K-polystability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | K-polystability and reduced uniform K-stability of log Fano cone singularities Wang, Linsheng Algebraic Geometry We prove that a log Fano cone $(X,Δ,ξ_0)$ satisfying $δ_\mathbb{T}(X,Δ,ξ_0)\ge 1$ 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 $(X,Δ,ξ_0)$ and show that it is equivalent to K-polystability. |
| title | K-polystability and reduced uniform K-stability of log Fano cone singularities |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2505.10828 |