A Supplement to the anticanonical Volumes of weak $\mathbb{Q}$-Fano threefolds of Picard rank two
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912249648513024 |
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| author | Lai, Ching-Jui Lee, Tsung-Ju |
| author_facet | Lai, Ching-Jui Lee, Tsung-Ju |
| contents | We show that for a weak $\mathbb{Q}$-Fano threefold $X$ ($\mathbb{Q}$-factorial with terminal singularities and $-K_X$ is nef and big) of Picard rank $ρ(X)\leq 2$, either $-K_X^3\leq 64$ or $-K_X^3=72$ and $X=\mathbb{P}_{\mathbb{P}^2}(\mathcal{O}_{\mathbb{P}^2}\oplus\mathcal{O}_{\mathbb{P}^2}(3))$. This is supplementary to the previous work in arXiv:2501.12555. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19419 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Supplement to the anticanonical Volumes of weak $\mathbb{Q}$-Fano threefolds of Picard rank two Lai, Ching-Jui Lee, Tsung-Ju Algebraic Geometry 14J30, 14J45, 14E30 We show that for a weak $\mathbb{Q}$-Fano threefold $X$ ($\mathbb{Q}$-factorial with terminal singularities and $-K_X$ is nef and big) of Picard rank $ρ(X)\leq 2$, either $-K_X^3\leq 64$ or $-K_X^3=72$ and $X=\mathbb{P}_{\mathbb{P}^2}(\mathcal{O}_{\mathbb{P}^2}\oplus\mathcal{O}_{\mathbb{P}^2}(3))$. This is supplementary to the previous work in arXiv:2501.12555. |
| title | A Supplement to the anticanonical Volumes of weak $\mathbb{Q}$-Fano threefolds of Picard rank two |
| topic | Algebraic Geometry 14J30, 14J45, 14E30 |
| url | https://arxiv.org/abs/2502.19419 |