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Curves on compact Shimura surfaces

组织者

刁晗生 , 杜衡 , 胡悦科 , Bin Xu , Yihang Zhu

演讲者

Zhehao Li

时间

2025年10月13日 10:00 至 11:00

地点

Shuangqing-B627

摘要

We investigate and compare the behaviors of complex curves on two types of compact Shimura surfaces: compact variants of Picard and Hilbert modular surfaces. We will see how complex curves of a fixed genus vanish when the defining discriminant of the Shimura surface grows, and how the special subvarieties and hyperbolic geometry play important roles in the proof. The results can be viewed as special cases of characteristic 0 function field analogs of uniform boundedness on the endomorphism types of abelian varieties.