中文摘要：

在这糊，环形圆纹曲面的差别变化的概念被定义，为环形圆纹曲面的差别变化的四相等的描述以差别被介绍由差别 tori 的合理 parametrization，差别坐标戒指，环形圆纹曲面的差别理想，和组行动。在环形圆纹曲面的差别变化之间的连接并且仿射[x ]-semimodules 被证明在无法缩减的不变的差别亚变种和脸之间的一对一的通讯建立[x ]-semimodules 和轨道脸通讯。最后，一个算法被给决定二项式的差别理想是否代表了由一[x ] 格子定义一个环形圆纹曲面的差别变化。

英文摘要：

In this paper, the concept of toric difference varieties is defined and four equivalent descriptions for toric difference varieties are presented in terms of difference rational parametrization, difference coordinate rings, toric difference ideals, and group actions by difference tori. Connections between toric difference varieties and affine N[x]-semimodules are established by proving the one-to-one correspondence between irreducible invariant difference subvarieties and faces of N[x]-semimodules and the orbit-face correspondence. Finally, an algorithm is given to decide whether a binomial difference ideal represented by a Z[x]-lattice defines a toric difference variety.