Toric Difference Variety

作     者：GAO Xiao-Shan HUANG Zhang WANG Jie YUAN Chun-Ming 

作者机构：Key Laboratory of Mathematics MechanizationAcademy of Mathematics and Systems ScienceChinese Academy of Sciences Department of Applied MathematicsChengdu University of Technology 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2017年第30卷第1期

页      面：173-195页

核心收录：

学科分类：0810[工学-信息与通信工程] 1205[管理学-图书情报与档案管理] 07[理学] 0811[工学-控制科学与工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China under Grant No.11688101 

主　　题：Afflne N[x]-semimodule difference torus T-orbit toirc difference ideal toric differencevariety Z[x]-lattice. 

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.