论文标题
具有许多自动形态和CM Jacobians的超椭圆形曲线
Superelliptic curves with many automorphisms and CM Jacobians
论文作者
论文摘要
令$ \ mathcal {c} $为平滑，投影，属$ g \ geq 2 $曲线，定义在$ \ mathbb {c} $上。然后，$ \ nathcal {c} $具有\ emph {许多自动形态学}，如果其相应的模量点$ p \ in \ mathcal {m} _g $ in \ mathcal {m} _g $在复杂的拓扑中都有一个邻居$ u $，以便所有曲线都与$ \ u \ u \ u \ u \ u \ u \ u \ u \ u \ u \ f { $ \ Mathcal {C} $。我们完全计算具有许多自动形态的超椭圆形曲线列表。对于这些曲线中的每一个，我们确定其Jacobian是否具有复杂的乘法。结果，我们证明了这些曲线的Streit复杂乘法标准的相反。
Let $\mathcal{C}$ be a smooth, projective, genus $g\geq 2$ curve, defined over $\mathbb{C}$. Then $\mathcal{C}$ has \emph{many automorphisms} if its corresponding moduli point $p \in \mathcal{M}_g$ has a neighborhood $U$ in the complex topology, such that all curves corresponding to points in $U \setminus \{p \}$ have strictly fewer automorphisms than $\mathcal{C}$. We compute completely the list of superelliptic curves having many automorphisms. For each of these curves, we determine whether its Jacobian has complex multiplication. As a consequence, we prove the converse of Streit's complex multiplication criterion for these curves.
