发表机构
Oakland University（奥克兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对特征零域上的绝对不可约平面曲线模型，提出一种算法，用于判定其属于超椭圆曲线轨迹的对应\\( n \\)值，计算其超椭圆模型及双有理变换。
AI 中文摘要
设\\( \mathcal{S}_{g,n} \subset \mathcal{M}_g \\)为亏格\\( g \geq 2 \\)且具有模型\\( y^n = h(x) \\)（其中\\( h \\)可分）的曲线轨迹；此类曲线\\( C \\)具有阶为\\( n \\)的循环群\\( C_n \leq \operatorname{Aut}(C) \\)，满足\\( C/C_n \cong \mathbb{P}^1 \\)。本文提出一种算法，给定特征零域\\( k_0 \\)上曲线\\( C \\)的绝对不可约平面模型\\( F(x,y) = 0 \\)，该算法可判定曲线属于\\( \mathcal{S}_{g,n} \\)的所有\\( n \\)值，并返回模型\\( y^n = h(x) \\)以及到该模型的双有理变换。
英文摘要
Let \( \mathcal{S}_{g,n} \subset \mathcal{M}_g \) be the locus of curves of genus \( g \geq 2 \) admitting a model \( y^n = h(x) \) with \( h \) separable; such curves $C$ have a cyclic group \( C_n \leq \operatorname{Aut}(C) \) of order \( n \) with \( C/C_n \cong \mathbb{P}^1 \). % We give an algorithm which, given an absolutely irreducible plane model \( F(x,y) = 0 \) of a curve \( C \) over a field \( k_0 \) of characteristic zero, decides for which \( n \) the curve lies in \( \mathcal{S}_{g,n} \) and returns a model \( y^n = h(x) \) together with the birational transformation to it.
