论文标题
单一模块化品种的反射性障碍物
Reflective obstructions of unitary modular varieties
论文作者
论文摘要
为了证明模块化的种类是一般类型的，有三种类型的障碍：反射性，尖和椭圆障碍物。在本文中，我们对统一案例的反射性障碍物进行定量估计。这特别表明，反射性障碍物在更高维度上足够小，例如$ 138 $。我们的结果减少了对统一模块化品种的Kodaira维度的研究，以定量的方式构建了尖锐的小重量形式。作为副产品，我们制定并部分证明了赫尔米利亚晶格的有限性，该遗传学晶格承认反射模块化形式，这是正交病例中Gritsenko-Nikulin对猜想的单一类似物。我们对反射障碍物的估计使用Prasad的音量公式。
To prove that a modular variety is of general type, there are three types of obstructions: reflective, cusp and elliptic obstructions. In this paper, we give a quantitative estimate of the reflective obstructions for the unitary case. This shows in particular that the reflective obstructions are small enough in higher dimension, say greater than $138$. Our result reduces the study of the Kodaira dimension of unitary modular varieties to the construction of a cusp form of small weight in a quantitative manner. As a byproduct, we formulate and partially prove the finiteness of Hermitian lattices admitting reflective modular forms, which is a unitary analog of the conjecture by Gritsenko-Nikulin in the orthogonal case. Our estimate of the reflective obstructions uses Prasad's volume formula.
