论文标题
嵌入雅各布人的曲线上给定顺序的扭转点数的界限
Bounds on the number of torsion points of given order on curves embedded in their jacobians
论文作者
论文摘要
在我们研究的任意特征的代数封闭领域上工作，对于整数，$ n \ geq 2 $和$ g \ geq 2 $，这是订购点的集合，将$ n $划分在不可减至的平滑曲线上，固定在雅各比族中，使用固定基点。我们讨论了其基数的界限，并描述了计算集合的有效方法。我们的方法使用与Weierstrass点研究中使用的方法相似的Wronskians，并且我们的边界的强度与曲线的某些倍数是否包含在Theta Divisor的负数中有关。讨论了几个例子。这概括了我们以前的工作[https://doi.org/10.1216/rmj.2023.53.357]，以使用WeierStrass点作为基本点来处理嵌入在Jacobian中的高纤维曲线的情况。
Working over an algebraically closed field of arbitrary characteristic we study, for integers $N\geq 2$ and $g\geq 2$, the set of points of order dividing $N$ lying on an irreducible smooth proper curve of genus $g$ embedded in its jacobian using a fixed base point. We discuss bounds on its cardinality and describe an efficient method for computing the set. Our method uses wronskians similar to those used in the study of Weierstrass points and the strength of our bounds is related to whether or not a certain multiple of the curve is contained in the negative of the theta divisor. Several examples are discussed. This generalizes our previous work [https://doi.org/10.1216/rmj.2023.53.357] dealing with the case of hyperelliptic curves embedded in their jacobian using a Weierstrass point as base point.
