English

On the dimension of systems of algebraic difference equations

Algebraic Geometry 2020-11-23 v2 Commutative Algebra

Abstract

We introduce a notion of dimension for the solution set of a system of algebraic difference equations that measures the degrees of freedom when determining a solution in the ring of sequences. This number need not be an integer, but, as we show, it satisfies properties suitable for a notion of dimension. We also show that the dimension of a difference monomial is given by the covering density of its set of exponents.

Keywords

Cite

@article{arxiv.2004.01596,
  title  = {On the dimension of systems of algebraic difference equations},
  author = {Michael Wibmer},
  journal= {arXiv preprint arXiv:2004.01596},
  year   = {2020}
}

Comments

28 pages, some corrections and more details added, mainly in Section 1