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Toric difference variety

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Abstract

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.

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Author information

Authors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Xiao-Shan Gao, Jie Wang & Chun-Ming Yuan

  2. Department of Applied Mathematics, Chengdu University of Technology, Chengdu, 610059, China

    Zhang Huang

Authors
  1. Xiao-Shan Gao
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  2. Zhang Huang
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  3. Jie Wang
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  4. Chun-Ming Yuan
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Corresponding author

Correspondence to Chun-Ming Yuan.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 11688101.

This paper was recommended for publication by Editor LI Hongbo.

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Gao, XS., Huang, Z., Wang, J. et al. Toric difference variety. J Syst Sci Complex 30, 173–195 (2017). https://doi.org/10.1007/s11424-017-6174-9

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  • DOI: https://doi.org/10.1007/s11424-017-6174-9

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