Characterizing terminal Fano threefolds with the smallest anti-canonical volume
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866916723788087296 |
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| author | Jiang, Chen |
| author_facet | Jiang, Chen |
| contents | It was proved by J. A. Chen and M. Chen that a terminal Fano $3$-fold $X$ satisfies $(-K_X)^3\geq \frac{1}{330}$. We show that a non-rational $\mathbb{Q}$-factorial terminal Fano $3$-fold $X$ with $ρ(X)=1$ and $(-K_X)^3=\frac{1}{330}$ is a weighted hypersurface of degree $66$ in $\mathbb{P}(1,5,6,22,33)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_03453 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Characterizing terminal Fano threefolds with the smallest anti-canonical volume Jiang, Chen Algebraic Geometry It was proved by J. A. Chen and M. Chen that a terminal Fano $3$-fold $X$ satisfies $(-K_X)^3\geq \frac{1}{330}$. We show that a non-rational $\mathbb{Q}$-factorial terminal Fano $3$-fold $X$ with $ρ(X)=1$ and $(-K_X)^3=\frac{1}{330}$ is a weighted hypersurface of degree $66$ in $\mathbb{P}(1,5,6,22,33)$. |
| title | Characterizing terminal Fano threefolds with the smallest anti-canonical volume |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2109.03453 |