AI 中文总结
本文综述关联等价性，它于1970年左右被引入以扩展曲线阿贝尔 - 雅可比映射性质。利用高维相关映射引发问题：几何关联等价与阿贝尔 - 雅可比等价是否相同？概述了相关结果及猜想，动机源于格里菲斯问题与阿基米德高度配对渐近行为的联系。
AI 中文摘要
本文是关于关联等价性的结果综述。关联等价性这一概念于1970年左右被引入，当时试图扩展曲线的阿贝尔 - 雅可比映射的经典性质。利用高维中的中间雅可比簇和相关的阿贝尔 - 雅可比映射，出现了一个自然问题：几何定义的关联等价关系是否与具有超越性质的阿贝尔 - 雅可比等价相同？本文概述了与该问题及一些尚未解决的经典猜想相关的结果，如格罗滕迪克的广义霍奇猜想。撰写此综述的动机来自最近观察到的格里菲斯问题与几何环境中阿基米德高度配对的渐近行为之间的意外联系。
英文摘要
This is a survey of results on incidence equivalence, a notion introduced by P$.$Griffiths around 1970 when trying to extend the classical properties of the Abel-Jacobi map for curves. Using the intermediate jacobians and the associated Abel-Jacobi maps in higher dimension, a natural question came up: is the geometrically defined incidence equivalence relation the same as Abel-Jacobi equivalence, which is of transcendental nature? I give an overview of results related to this question and to several classical conjectures that are far from resolved, such as Grothendieck's generalized Hodge conjecture. The motivation for writing this survey came from a recently observed unexpected connection of Griffiths' question to the asymptotic behaviour of the archimedean height pairing in a geometric setting.
Comments17 pages
