论文标题
单一Shimura品种的奇异性和Kodaira尺寸
The singularities and Kodaira dimension of unitary Shimura varieties
论文作者
论文摘要
许多人都研究了Shimura品种的Kodaira尺寸。 Kondo和Gritsenko-Hulek-Sankaran研究了与极化K3表面的模量空间相关的正交Shimura品种的奇异性。他们证明了它们具有规范的奇异性，如果极化程度足够大，则具有一般类型。在本文中，我们为单一shimura品种处理类似的问题。我们表明，如果$ n> 4 $，它们具有规范的奇异性。作为一个应用程序，我们表明，某些与Hermitian形式相关的统一shimura品种在$ \ mathbb {q}}（\ sqrt {-1}）$，$ \ mathbb {q}（\ sqrt {-3}）$的整数上的整数相关。我们使用在RAMIFIENT分隔符上使用模块化的低重量消失形式，这是Borcherds形式的准折叠式限制$φ_{12} $。
The Kodaira dimension of Shimura varieties has been studied by many people. Kondo and Gritsenko-Hulek-Sankaran studied the singularities of orthogonal Shimura varieties related to the moduli spaces of polarized K3 surfaces. They proved that they have canonical singularities and are of general type if the polarization degree is sufficiently large. In this paper, we work on similar problems for unitary Shimura varieties. We show that they have canonical singularities if $n > 4$. As an application, we show that certain unitary Shimura varieties associated with Hermitian forms over the rings of integers of $\mathbb{Q}(\sqrt{-1})$, $\mathbb{Q}(\sqrt{-3})$ are of general type. We use modular forms of low weight vanishing on ramification divisors, which are the restrictions of the quasi-pullbacks of the Borcherds form $Φ_{12}$.
