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