Let $m$ be a positive integer and $q$ be a prime power. For large finite base fields $\mathbb F_q$, we show that any curve can be used to produce a complete $m$-arc as long as some generic explicit geometric conditions on the curve are verified. To show the effectiveness of our theory, we derive complete $m$-arcs from hyperelliptic curves and from Artin-Schreier curves.

翻译：当$ m $是正整数且$ q $是素数幂时，对于大的有限基域$ \mathbb F_q $，我们表明只要验证曲线上一些通用的显式几何条件，则可以使用任何曲线生成完整的$ m $-弧。为了展示我们理论的有效性，我们从超椭圆曲线和Artin-Schreier曲线中导出完整的$ m $-弧。