Uniform K-stability of $G$-varieties of complexity 1
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911227118092288 |
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| author | Li, Yan Li, Zhenye |
| author_facet | Li, Yan Li, Zhenye |
| contents | Let ${\rm k}$ be an algebraically closed field of characteristic 0 and $G$ a connect, reductive group over it. Let $X$ be a projective $G$-variety of complexity 1. We classify $G$-equivariant normal test configurations of $X$ with integral central fibre via the combinatorial data. We also give a formula of anti-canonical divisors on $X$. Based on this formula, when $X$ is $\mathbb Q$-Fano, we give an expression of the Futaki invariant, and derive a criterion of uniform K-stability in terms of the combinatorial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14901 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform K-stability of $G$-varieties of complexity 1 Li, Yan Li, Zhenye Algebraic Geometry Differential Geometry Let ${\rm k}$ be an algebraically closed field of characteristic 0 and $G$ a connect, reductive group over it. Let $X$ be a projective $G$-variety of complexity 1. We classify $G$-equivariant normal test configurations of $X$ with integral central fibre via the combinatorial data. We also give a formula of anti-canonical divisors on $X$. Based on this formula, when $X$ is $\mathbb Q$-Fano, we give an expression of the Futaki invariant, and derive a criterion of uniform K-stability in terms of the combinatorial data. |
| title | Uniform K-stability of $G$-varieties of complexity 1 |
| topic | Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2407.14901 |