On K-stability of Fano weighted hypersurfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916102121979904 |
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| author | Sano, Taro Tasin, Luca |
| author_facet | Sano, Taro Tasin, Luca |
| contents | Let $X \subset \mathbb P(a_0,\ldots,a_n)$ be a quasi-smooth weighted Fano hypersurface of degree $d$ and index $I_X$ such that $a_i |d$ for all $i$, with $a_0 \le \ldots \le a_n$. If $I_X=1$, we show that, under a suitable condition, the $α$-invariant of $X$ is greater than or equal to $\dim X/(\dim X+1)$ and $X$ is K-stable. This can be applied in particular to any $X$ as above such that $\dim X \le 3$. If $X$ is general and $I_X < \dim X$, then we show that $X$ is K-stable. We also give a sufficient condition for the finiteness of automorphism groups of quasi-smooth Fano weighted complete intersections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_15209 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On K-stability of Fano weighted hypersurfaces Sano, Taro Tasin, Luca Algebraic Geometry Let $X \subset \mathbb P(a_0,\ldots,a_n)$ be a quasi-smooth weighted Fano hypersurface of degree $d$ and index $I_X$ such that $a_i |d$ for all $i$, with $a_0 \le \ldots \le a_n$. If $I_X=1$, we show that, under a suitable condition, the $α$-invariant of $X$ is greater than or equal to $\dim X/(\dim X+1)$ and $X$ is K-stable. This can be applied in particular to any $X$ as above such that $\dim X \le 3$. If $X$ is general and $I_X < \dim X$, then we show that $X$ is K-stable. We also give a sufficient condition for the finiteness of automorphism groups of quasi-smooth Fano weighted complete intersections. |
| title | On K-stability of Fano weighted hypersurfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2111.15209 |