标题： 无挠球商的余阿贝尔环面紧化 显示英文标题

标题： Co-abelian toroidal compactifications of torsion free ball quotients

摘要： 设 X' 是复 2-球关于 SU(2,1) 的无挠格子 Γ 的商的环面紧致化。我们说 X' 是余阿贝尔的，如果存在一个与 X' 双有理等价的阿贝尔曲面。 本文可以看作是对大量非紧致余阿贝尔无挠环面紧致化的存在的一个说明。 更具体地说，它表明所有无挠复 2-球商的容许体积值都被艾森斯坦数上的余阿贝尔皮卡德模态的那些实现。 文章提供了三类无限序列的有限无分歧覆盖，这些覆盖是艾森斯坦数上的余阿贝尔、无挠、皮卡德模态环面紧致化，其体积无限增加。 第一类由具有固定尖点数且彼此双有理等价的成员支持。 第二类由彼此双有理等价且尖点数无限增加的项组成。 第三类序列涉及彼此非双有理等价的环面紧致化，其尖点数无限增加。 显示英文摘要

摘要： Let X' be the toroidal compactification of the quotient of the complex 2-ball by a torsion free lattice G of SU(2,1). We say that X'is co-abelian if there is an abelian surface, birational to X'. The present work can be viewed as an illustration for the presence of a plenty of non-compact co-abelian torsion free toroidal compactifications. More precisely, it shows that all the admissible values for the volume of a torsion free quotient of the complex 2-ball are attained by co-abelian Picard modular ones over Eisenstein numbers. The article provides three types of infinite series of finite unramified coverings of co-abelian, torsion free, Picard modular toroidal compactifications over Eisenstein numbers, with infinitely increasing volumes. The first type is supported by mutually birational members with fixed number of cusps. The second kind is with mutually birational terms and infinitely increasing number of cusps. The third kind of series relates mutually non-birational toroidal compactifications with infinitely increasing number of cusps.