Toric Difference Variety
Symbolic Computation
2016-04-08 v1 Algebraic Geometry
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 correspondence between the irreducible invariant difference subvarieties and the faces of the N[x]-submodules 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.
Cite
@article{arxiv.1604.01958,
title = {Toric Difference Variety},
author = {Xiao-Shan Gao and Zhang Huang and Jie Wang and Chun-Ming Yuan},
journal= {arXiv preprint arXiv:1604.01958},
year = {2016}
}