Large orders of automorphisms of smooth curves in $\mathbb P^1\times \mathbb P^1$

Taro Hayashi; Keika Shimahara

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arXiv · 2512.14948

Large orders of automorphisms of smooth curves in $\mathbb P^1\times \mathbb P^1$

Taro Hayashi·Keika Shimahara

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Abstract

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 $\mathbb P^1$.

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BibTeX RIS

Taro Hayashi, Keika Shimahara. 2025-12-16. Large orders of automorphisms of smooth curves in $\mathbb P^1\times \mathbb P^1$. https://arxiv.org/abs/2512.14948

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