On birational boundedness of foliated surfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866915096109776896 |
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| author | Hacon, Christopher D. Langer, Adrian |
| author_facet | Hacon, Christopher D. Langer, Adrian |
| contents | In this paper we prove a result on the effective generation of pluri-canonical linear systems on foliated surfaces of general type. Fix a function $P: \mathbb Z_{\geq 0}\to \mathbb Z $, then there exists an integer $N_1>0$ such that if $(X,\mathcal F)$ is a canonical or nef model of a foliation of general type with Hilbert polynomial $χ(X, mK_{\mathcal F})=P(m)$ for all $m\in \mathbb Z_{\geq 0}$, then $|mK_{\mathcal F}|$ defines a birational map for all $m\geq N_1$.
We also prove a Grauert-Riemannschneider type vanishing theorem for foliated surfaces with canonical singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_07709 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On birational boundedness of foliated surfaces Hacon, Christopher D. Langer, Adrian Algebraic Geometry In this paper we prove a result on the effective generation of pluri-canonical linear systems on foliated surfaces of general type. Fix a function $P: \mathbb Z_{\geq 0}\to \mathbb Z $, then there exists an integer $N_1>0$ such that if $(X,\mathcal F)$ is a canonical or nef model of a foliation of general type with Hilbert polynomial $χ(X, mK_{\mathcal F})=P(m)$ for all $m\in \mathbb Z_{\geq 0}$, then $|mK_{\mathcal F}|$ defines a birational map for all $m\geq N_1$. We also prove a Grauert-Riemannschneider type vanishing theorem for foliated surfaces with canonical singularities. |
| title | On birational boundedness of foliated surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1910.07709 |