The canonical map of a foliated surface of general type
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929537724448768 |
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| author | Lü, Xin |
| author_facet | Lü, Xin |
| contents | Let $(S,\mathcal{F})$ be a foliated surface over the complex number of general type, i.e., the Kodaira dimension $\mathrm{Kod}(\mathcal{F})=2$. We study the geometry of the canonical map $φ$ of the foliated surface $(S,\mathcal{F})$, and prove several boundedness results on the canonical map $φ$, generalizing Beauville's beautiful work on the canonical maps of algebraic surfaces to foliated surfaces. As an application, we prove three Noether type inequalities for $(S,\mathcal{F})$ depending on the Kodaira dimension of the surface $S$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The canonical map of a foliated surface of general type Lü, Xin Algebraic Geometry Let $(S,\mathcal{F})$ be a foliated surface over the complex number of general type, i.e., the Kodaira dimension $\mathrm{Kod}(\mathcal{F})=2$. We study the geometry of the canonical map $φ$ of the foliated surface $(S,\mathcal{F})$, and prove several boundedness results on the canonical map $φ$, generalizing Beauville's beautiful work on the canonical maps of algebraic surfaces to foliated surfaces. As an application, we prove three Noether type inequalities for $(S,\mathcal{F})$ depending on the Kodaira dimension of the surface $S$. |
| title | The canonical map of a foliated surface of general type |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2410.08465 |