具有大素数平方阶自同构群的代数曲线
Algebraic curves admitting automorphism groups of large prime square order
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中文总结 AI 辅助
针对任意特征代数闭域上的曲线，本文给出了自同构群阶为素数平方的素数界、对应曲线族分类及最高界曲线的完全自同构群。
中文摘要 AI 辅助
设𝕂为任意特征的代数闭域，本文对存在定义在𝕂上且自同构群阶为ℓ²的曲线的素数ℓ的大小给出了界；此外，还对在驯顺与非驯顺情形下达到ℓ上界的曲线族进行了分类；最后，给出了达到最高界的曲线的完全自同构群。
英文摘要
Let $\mathbb{K}$ denote an algebraically closed field of arbitrary characteristic. In this paper we provide bounds for the size of a prime $\ell$ for which there are curves defined over $\mathbb{K}$ admitting automorphism groups of order $\ell^2$. In addition, we also give a classification of the families of curves attaining the upper bounds for $\ell$ in both tame and wild case. Finally, we present the full automorphism groups of the curves attaining the highest bounds.
