论文标题
在第三属曲线及其应用的曲线上有些明确的算术
Some explicit arithmetic on curves of genus three and their applications
论文作者
论文摘要
雅各布品种之间的richelot同性恋是一种同等基因，其内核包含在该域的$ 2 $ torsion子组中。 Richelot的同源物是两个或多个主要两极化的Abelian品种的产物，称为分解的Richelot同等基因。 在本文中，我们在$ 3 $的曲线上开发了一些明确的算术，其中包括计算分解的Richelot同等基因的算法。作为计算分解的Richelot同等基因的域的解决方案，还提供了定义方程式的明确公式，用于$ 3 $的Howe曲线。使用公式，我们将构建一种具有复杂性$ \ tilde {o}（p^3）$（分别$ \ tilde {o}（p^4）$）的算法，以枚举所有高ellirtictic（sept。Nonthyperelliptriptic）supperspecial opperspecial opperspecial ofsperspecial howe now of $ 3 $ 3 $ 3 $ 3 $。
A Richelot isogeny between Jacobian varieties is an isogeny whose kernel is included in the $2$-torsion subgroup of the domain. A Richelot isogeny whose codomain is the product of two or more principally polarized abelian varieties is called a decomposed Richelot isogeny. In this paper, we develop some explicit arithmetic on curves of genus $3$, including algorithms to compute the codomain of a decomposed Richelot isogeny. As solutions to compute the domain of a decomposed Richelot isogeny, explicit formulae of defining equations for Howe curves of genus $3$ are also given. Using the formulae, we shall construct an algorithm with complexity $\tilde{O}(p^3)$ (resp. $\tilde{O}(p^4)$) to enumerate all hyperelliptic (resp. non-hyperelliptic) superspecial Howe curves of genus $3$.
