Log K-stability of GIT-stable divisors on Fano varieties
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866916548636049408 |
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| author | Zhou, Chuyu |
| author_facet | Zhou, Chuyu |
| contents | For a given K-polystable Fano variety $X$ and a natural number $l$ such that $(X, \frac{1}{l} B)$ is log canonical for some $B\in |-lK_X|$, we show that there exists a rational number $0<c_1<1$ depending only on $X$ and $l$, such that $D\in |-lK_X|$ is GIT-(semi/poly)stable under the action of Aut(X) if and only if the pair $(X, \fracε{l}D)$ is K-(semi/poly)stable for some rational $0<ε<c_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_07458 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Log K-stability of GIT-stable divisors on Fano varieties Zhou, Chuyu Algebraic Geometry 14J10, 14J45 For a given K-polystable Fano variety $X$ and a natural number $l$ such that $(X, \frac{1}{l} B)$ is log canonical for some $B\in |-lK_X|$, we show that there exists a rational number $0<c_1<1$ depending only on $X$ and $l$, such that $D\in |-lK_X|$ is GIT-(semi/poly)stable under the action of Aut(X) if and only if the pair $(X, \fracε{l}D)$ is K-(semi/poly)stable for some rational $0<ε<c_1$. |
| title | Log K-stability of GIT-stable divisors on Fano varieties |
| topic | Algebraic Geometry 14J10, 14J45 |
| url | https://arxiv.org/abs/2102.07458 |