K-stability of Fano weighted hypersurfaces via plt flags and convex geometry
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908750136213504 |
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| author | Campo, Livia Fujita, Kento Sano, Taro Tasin, Luca |
| author_facet | Campo, Livia Fujita, Kento Sano, Taro Tasin, Luca |
| contents | We develop a framework to study the K-stability of weighted Fano hypersurfaces based on a combination of birational and convex-geometric techniques. As an application, we prove that all quasi-smooth weighted Fano hypersurfaces of index 1 with at most two weights greater than 1 are K-stable. We also construct several examples of K-unstable quasi-smooth weighted Fano hypersurfaces of low indices. To prove these results, we establish lower bounds for stability thresholds using the method of Abban-Zhuang, which reduces the problem to lower-dimensional cases. A key feature of our approach is the use of plt flags that are not necessarily admissible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02974 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | K-stability of Fano weighted hypersurfaces via plt flags and convex geometry Campo, Livia Fujita, Kento Sano, Taro Tasin, Luca Algebraic Geometry We develop a framework to study the K-stability of weighted Fano hypersurfaces based on a combination of birational and convex-geometric techniques. As an application, we prove that all quasi-smooth weighted Fano hypersurfaces of index 1 with at most two weights greater than 1 are K-stable. We also construct several examples of K-unstable quasi-smooth weighted Fano hypersurfaces of low indices. To prove these results, we establish lower bounds for stability thresholds using the method of Abban-Zhuang, which reduces the problem to lower-dimensional cases. A key feature of our approach is the use of plt flags that are not necessarily admissible. |
| title | K-stability of Fano weighted hypersurfaces via plt flags and convex geometry |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.02974 |