Toric difference variety

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• 作者：Xiao-Shan Gao ; Zhang Huang ; Jie Wang…
• 关键词：Affine ℕ[x] ; semimodule ; difference torus ; T ; orbit ; toirc difference ideal ; toric difference variety ; ℤ[x] ; lattice
• 刊名：Journal of Systems Science and Complexity
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：30
• 期：1
• 页码：173-195
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory, Control; Operation Research/Decision Theory; Mathematics of Computing; Complex Systems; Statistics, general;
• 出版者：Academy of Mathematics and Systems Science, Chinese Academy of Sciences
• ISSN：1559-7067
• 卷排序：30

文摘

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.