Numerical conditions for the boundedness of foliated surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913601202159616 |
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| author | Passantino, Alessandro |
| author_facet | Passantino, Alessandro |
| contents | We show that the set of Hilbert functions $P(m)=χ(mK_\mathcal{F})$ of 2-dimensional foliated canonical models with fixed $K_\mathcal{F}^2$, $K_\mathcal{F} \cdot K_X$ and $i_\mathbb{Q}(\mathcal{F})$ is finite. As a consequence, we deduce that two results on the effective birationality and boundedness of foliated canonical models with fixed Hilbert function still hold when only $K_\mathcal{F}^2$, $K_\mathcal{F} \cdot K_X$ and $i_\mathbb{Q}(\mathcal{F})$ are fixed. We then give examples further investigating the properties of families of canonical models, and study particular cases in which some of the conditions are not necessary. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_05986 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical conditions for the boundedness of foliated surfaces Passantino, Alessandro Algebraic Geometry 14J10, 37F75 We show that the set of Hilbert functions $P(m)=χ(mK_\mathcal{F})$ of 2-dimensional foliated canonical models with fixed $K_\mathcal{F}^2$, $K_\mathcal{F} \cdot K_X$ and $i_\mathbb{Q}(\mathcal{F})$ is finite. As a consequence, we deduce that two results on the effective birationality and boundedness of foliated canonical models with fixed Hilbert function still hold when only $K_\mathcal{F}^2$, $K_\mathcal{F} \cdot K_X$ and $i_\mathbb{Q}(\mathcal{F})$ are fixed. We then give examples further investigating the properties of families of canonical models, and study particular cases in which some of the conditions are not necessary. |
| title | Numerical conditions for the boundedness of foliated surfaces |
| topic | Algebraic Geometry 14J10, 37F75 |
| url | https://arxiv.org/abs/2412.05986 |