标题： 托里奇流形和牛顿多边形 显示英文标题

标题： The Torelli locus and Newton polygons

摘要： 本文是关于曲线的雅可比簇的阿贝尔簇。 我开始撰写此文是为了2024年亚利桑那冬季学校关于阿贝尔簇的讲座系列。 一个更长且描述性更强的标题可能是：阿贝尔簇模空间中的托雷利轨迹，以及在正特征中曲线的牛顿多边形的应用。 具体来说，本文涵盖了两个主题：第一个是关于托雷利轨迹的几何；第二个是关于在正特征中光滑曲线的雅可比簇所出现的算术不变量。 显示英文摘要

摘要： This manuscript is about abelian varieties that are Jacobians of curves. I started writing it for a lecture series at the Arizona Winter School in 2024 on abelian varieties. A longer more descriptive title might be: The Torelli locus in the moduli space of abelian varieties, with applications to Newton polygons of curves in positive characteristic. To elaborate, this manuscript covers two topics: the first is about the geometry of the Torelli locus; the second is about the arithmetic invariants of abelian varieties that occur for Jacobians of smooth curves in positive characteristic.