Logarithmic multicanonical systems of smooth affine surfaces of logarithmic Kodaira dimension one
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917639363756032 |
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| author | Kojima, Hideo |
| author_facet | Kojima, Hideo |
| contents | Let $S$ be a smooth affine surface of logarithmic Kodaira dimension one and let $(V,D)$ be a pair of a smooth projective surface $V$ and a simple normal crossing divisor $D$ on $V$ such that $V \setminus \operatorname{Supp} D = S$. In this paper, we consider the logarithmic multicanonical system $|m(K_V + D)|$. We prove that, for any $m \geq 8$, $|m(K_V+D)|$ gives an $\mathbb{P}^1$-fibration form $V$ onto a smooth projective curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09208 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Logarithmic multicanonical systems of smooth affine surfaces of logarithmic Kodaira dimension one Kojima, Hideo Algebraic Geometry Let $S$ be a smooth affine surface of logarithmic Kodaira dimension one and let $(V,D)$ be a pair of a smooth projective surface $V$ and a simple normal crossing divisor $D$ on $V$ such that $V \setminus \operatorname{Supp} D = S$. In this paper, we consider the logarithmic multicanonical system $|m(K_V + D)|$. We prove that, for any $m \geq 8$, $|m(K_V+D)|$ gives an $\mathbb{P}^1$-fibration form $V$ onto a smooth projective curve. |
| title | Logarithmic multicanonical systems of smooth affine surfaces of logarithmic Kodaira dimension one |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2404.09208 |