标题： 三维球面商 显示英文标题

标题： A three dimensional ball quotient

摘要： 在我们之前关于西格尔三折叠的研究中，考虑了属于酉群$\U(1,3)$的球面商。在本文中，我们确定了一个非常特殊的典范模形式簇的例子。实际上，我们确定了模形式环。这个代数有 25 个生成元，其中 15 个是一阶模形式$B_i$和十个是二阶模形式$C_j$。两者都将以 Borcherds 乘积的形式出现。我们确定了关系理想。形式$C_i$是尖点形式。它们的平方定义了非奇异模型上的全纯微分形式。 显示英文摘要

摘要： In connection with our previous investigation about Siegel threefolds which admit a Calabi--Yau model, we consider ball quotients which belong to the unitary group $\U(1,3)$. In this paper we determine a very particular example of a Picard modular variety of general type. Really we determine the ring of modular forms. This algebra has 25 generators, 15 modular forms $B_i$ of weight one and ten modular forms $C_j$ of weight 2. Both will appear as Borcherds products. We determine the ideal of relations. The forms $C_i$ are cuspidal. Their squares define holomorphic differential forms on the non-singular models.