Classification of threefold canonical thresholds
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929597783736320 |
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| author | Chen, Jheng-Jie Chen, Jiun-Cheng Wu, Hung-Yi |
| author_facet | Chen, Jheng-Jie Chen, Jiun-Cheng Wu, Hung-Yi |
| contents | We show that the set $\mathcal{T}_{3, \mathrm{sm}}^{\mathrm{can}}$ of smooth threefold canonical thresholds coincides with $\mathcal{T}_{2, \mathrm{sm}}^{\mathrm{lc}}=\mathcal{HT}_{2}$, where $\mathcal{HT}_{2}$ is the $2$-dimensional hypersurface log canonical thresholds characterized by Kuwata \cite{K99a, K99b}. We classify the set $\mathcal{T}_{3}^{\mathrm{can}}$ of threefold canonical thresholds. More precisely, we prove $\mathcal{T}_{3}^{\mathrm{can}}= \{0\} \cup \{\frac{4}{5}\} \cup \mathcal{T}_{3, \mathrm{sm}}^{\mathrm{can}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12373 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of threefold canonical thresholds Chen, Jheng-Jie Chen, Jiun-Cheng Wu, Hung-Yi Algebraic Geometry We show that the set $\mathcal{T}_{3, \mathrm{sm}}^{\mathrm{can}}$ of smooth threefold canonical thresholds coincides with $\mathcal{T}_{2, \mathrm{sm}}^{\mathrm{lc}}=\mathcal{HT}_{2}$, where $\mathcal{HT}_{2}$ is the $2$-dimensional hypersurface log canonical thresholds characterized by Kuwata \cite{K99a, K99b}. We classify the set $\mathcal{T}_{3}^{\mathrm{can}}$ of threefold canonical thresholds. More precisely, we prove $\mathcal{T}_{3}^{\mathrm{can}}= \{0\} \cup \{\frac{4}{5}\} \cup \mathcal{T}_{3, \mathrm{sm}}^{\mathrm{can}}$. |
| title | Classification of threefold canonical thresholds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2411.12373 |