曲线算术模空间上的微积分

Calculus on arithmetic moduli of curves

本文通过Abel-Jacobi映射、Poincaré单值化和Mumford稳定投影嵌入给出曲线模空间上的度量化线丛的三种构造.我们还描述了两个算术应用:一个是袁新意关于一致Bogomolov猜想的应用,另一个是我们与高紫阳合作关于Gross-Shoen闭链和Ceresa闭链的Northcott性质的应用.

We survey three constructions of metrized line bundles on the moduli of curves by means of Abel-Jacobi maps,uniformizations,and projective embeddings.We also describe two arithmetic applications:one to the uniform Bogomolov conjecture by Xinyi Yuan and the other to the Northcott property for Gross-Schoen cycles and Ceresa cycles.