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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.14948 |
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| _version_ | 1866909966615445504 |
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| author | Hayashi, Taro Shimahara, Keika |
| author_facet | Hayashi, Taro Shimahara, Keika |
| contents | For $a,b\geq 3$, we calculate the orders of automorphisms of smooth curves with bidegree $(a,b)$ in the product $\pp$ of the projective line $\mathbb P^1$. We identify smooth curves in $\pp$ which have automorphisms with the largest orders. In addition, we study the relationship between symmetry and geometric structure of curves. We provide a sufficient condition for the quotient space by an automorphism to be $\mathbb P^1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large orders of automorphisms of smooth curves in $\mathbb P^1\times \mathbb P^1$ Hayashi, Taro Shimahara, Keika Algebraic Geometry For $a,b\geq 3$, we calculate the orders of automorphisms of smooth curves with bidegree $(a,b)$ in the product $\pp$ of the projective line $\mathbb P^1$. We identify smooth curves in $\pp$ which have automorphisms with the largest orders. In addition, we study the relationship between symmetry and geometric structure of curves. We provide a sufficient condition for the quotient space by an automorphism to be $\mathbb P^1$. |
| title | Large orders of automorphisms of smooth curves in $\mathbb P^1\times \mathbb P^1$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.14948 |