标题： 有限阿贝尔群在有理连通三维流形上的作用 I：乘积型群 显示英文标题

标题： Finite abelian groups acting on rationally connected threefolds I: Groups of product type

摘要： 我们开始研究忠实作用在三维有理连通流形上的有限阿贝尔群。 我们证明这些群可以自然地分为三种类型：乘积类型的群是有限阿贝尔群，它们分别是属于1阶和2阶Cremona群的两个群的乘积；K3类型的群是由作用在K3曲面上的有限阿贝尔群的循环扩张组成；第三种类型的群是作用在终端Fano三维流形上的群，其反规范线性系统为空。 乘积类型群的分类来源于J. Blanc的一个结果。 对于K3类型的群，我们证明只有有限多个这样的群。 我们还提出了关于第三种类型群的一个猜想。 显示英文摘要

摘要： We initiate the study of finite abelian groups that faithfully act on 3-dimensional rationally connected varieties. We show that these groups can be naturally divided into three types: the groups of product type are finite abelian groups that are products of two groups which belong to the Cremona group of rank 1 and 2, respectively; the group of K3 type consists of cyclic extensions of finite abelian groups acting on a K3 surface; the third type consists of groups that act on terminal Fano threefolds with empty anti-canonical linear system. The classification of groups of product type follows from a result of J. Blanc. For the groups of K3 type, we show that there are only finitely many of them. We also formulate a conjecture regarding the groups of the third type.