Special subvarieties of non-arithmetic ball quotients and Hodge theory

• 成果类型: Article
• 署名作者: Baldi, Gregorio; Ullmo, Emmanuel
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2023.197.1.3
• 发表日期: 2023
• 页码: 159-220
• 关键词: hyperbolic space-forms; discrete subgroups; total geodesy; superrigidity; lattices; compactification; REPRESENTATIONS; conjecture; geometry; compact

摘要

Let Gamma subset of PU(1, n) be a lattice and Sr be the associated ball quotient. We prove that, if Sr contains infinitely many maximal complex totally geodesic subvarieties, then Gamma is arithmetic. We also prove an Ax-Schanuel Conjecture for Sr, similar to the one recently proven by Mok, Pila and Tsimerman. One of the main ingredients in the proofs is to realise Sr inside a period domain for polarised integral variations of Hodge structure and interpret totally geodesic subvarieties as unlikely intersections.