AI 中文总结
该研究刻画了作为球商栈紧化的光滑真Deligne-Mumford栈，证明了球商紧化的边界除子结构，推广了Deng-Cadorel的结果，所用方法结合了非阿贝尔霍奇对应等理论。
AI 中文摘要
我们对作为球商栈[ℬᵈ/Γ]的紧化而产生的光滑真Deligne-Mumford栈𝒳进行刻画。此外，我们证明每个球商都存在一个紧化，其边界除子𝒟:=𝒳−[ℬᵈ/Γ]是商栈[A/G]的不交并，其中A为阿贝尔簇，G为有限群。这推广了Deng-Cadorel的一个结果。我们的策略结合了光滑真DM-栈的Simpson非阿贝尔霍奇对应、Mochizuki将经典Simpson对应推广到对数情形的结果，以及Deng-Cadorel的单值化结果。
英文摘要
We characterize smooth proper Deligne-Mumford stacks $\mathscr{X}$ that arise as compactifications of ball quotient stacks $[\mathbb{B}^d/Γ]$. Moreover, we show that every ball quotient admits a compactification whose boundary divisor $\mathscr{D}:=\mathscr{X}-[\mathbb{B}^d/Γ]$ is a disjoint union of quotient stacks $[A/G]$, where $A$ is an abelian variety and $G$ is a finite group. This generalizes a result of Deng-Cadorel. Our strategy combines Simpson's non-abelian Hodge correspondence for smooth proper DM-stacks, Mochizuki's generalization of the classical Simpson's correspondence to the log setting, and the uniformization results of Deng-Cadorel.
Comments17 pages, comments welcome
