论文标题
计算五属的二进制曲线
Computing binary curves of genus five
论文作者
论文摘要
5属曲线可以是过度纤维化，三角形或非hyperelliptic非三角形，其模型是$ \ mathbb {p}^4 $中三个四边形的完整相交。我们介绍并解释了我们用来确定的算法，直到$ \ mathbb {f} _2 $上的同构，所有属5曲线属于$ \ mathbb {f} _2 $，我们分别为三种提到的类型中的每一种做到这一点。我们考虑了这些曲线，从$ \ mathbb {f} _2 $的Jacobians或牛顿多边形的$ \ mathbb {f} _2 $方面，对于三种类型中的每一种，我们计算了$ \ mathbb {f} _2 _2 _2 $ $ \ \ \ \ \ \ \ \ \ \ \ \ m i \ {f} _2 $ -Aut-aut的大小。
Genus 5 curves can be hyperelliptic, trigonal, or non-hyperelliptic non-trigonal, whose model is a complete intersection of three quadrics in $\mathbb{P}^4$. We present and explain algorithms we used to determine, up to isomorphism over $\mathbb{F}_2$, all genus 5 curves defined over $\mathbb{F}_2$, and we do that separately for each of the three mentioned types. We consider these curves in terms of isogeny classes over $\mathbb{F}_2$ of their Jacobians or their Newton polygons, and for each of the three types, we compute the number of curves over $\mathbb{F}_2$ weighted by the size of their $\mathbb{F}_2$-automorphism groups.
