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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1811.10421 |
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| _version_ | 1866915128151113728 |
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| author | Cai, Wenyi Qian, Yuanyuan Xiao, Hao Zhuo, Lingyu |
| author_facet | Cai, Wenyi Qian, Yuanyuan Xiao, Hao Zhuo, Lingyu |
| contents | Suppose $f:S\rightarrow\mathbb{P}^1$ is a surface fibration of genus $g$ with $3$ singular fibers. If two of the singular fibers are semistable, Nguyen conjectured that $f$ does not exist for $g\ge2$. However, a counterexample for $g=2$ was discovered by Gong-Lu-Tan. Note that such kind of surface fibrations admit strong arithmetic properties but are rare in fact, and as such the counterexamples are important. In this paper, we construct a new one for $g=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_10421 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A new counterexample to Nguyen's conjecture on surface fibration Cai, Wenyi Qian, Yuanyuan Xiao, Hao Zhuo, Lingyu Algebraic Geometry Suppose $f:S\rightarrow\mathbb{P}^1$ is a surface fibration of genus $g$ with $3$ singular fibers. If two of the singular fibers are semistable, Nguyen conjectured that $f$ does not exist for $g\ge2$. However, a counterexample for $g=2$ was discovered by Gong-Lu-Tan. Note that such kind of surface fibrations admit strong arithmetic properties but are rare in fact, and as such the counterexamples are important. In this paper, we construct a new one for $g=2$. |
| title | A new counterexample to Nguyen's conjecture on surface fibration |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1811.10421 |