Slopes of fibrations with trivial vertical fundamental groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916227697344512 |
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| author | Liu, Xiao-Lei Lu, Xin |
| author_facet | Liu, Xiao-Lei Lu, Xin |
| contents | Kodaira fibrations have non-trivial vertical fundamental groups and their slopes are all $12$. In this paper, we show that $12$ is indeed the sharp upper bound for the slopes of fibrations with trivial vertical fundamental groups. Precisely, for each $g\geq3$ we prove the existence of fibrations of genus $g$ with trivial vertical fundamental groups whose slopes can be arbitrarily close to $12$. This gives a relative analogy of Roulleau-Urzúa's work on the slopes of surfaces of general type with trivial fundamental groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_18341 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Slopes of fibrations with trivial vertical fundamental groups Liu, Xiao-Lei Lu, Xin Algebraic Geometry Kodaira fibrations have non-trivial vertical fundamental groups and their slopes are all $12$. In this paper, we show that $12$ is indeed the sharp upper bound for the slopes of fibrations with trivial vertical fundamental groups. Precisely, for each $g\geq3$ we prove the existence of fibrations of genus $g$ with trivial vertical fundamental groups whose slopes can be arbitrarily close to $12$. This gives a relative analogy of Roulleau-Urzúa's work on the slopes of surfaces of general type with trivial fundamental groups. |
| title | Slopes of fibrations with trivial vertical fundamental groups |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2404.18341 |