English

Vanishing Ideals Of Affine Sets Parameterized By Odd Cycles

Commutative Algebra 2017-11-01 v1

Abstract

Let K be a finite field. Let X* be a subset of the affine space Kn, which is parameterized by odd cycles. In this paper we give an explicit Gr\"obner basis for the vanishing ideal, I(X*), of X*. We give an explicit formula for the regularity of I(X*) and finally if X* is parameterized by an odd cycle of length k, we show that the Hilbert function of the vanishing ideal of X* can be written as linear combination of Hilbert functions of degenerate torus.

Keywords

Cite

@article{arxiv.1710.11314,
  title  = {Vanishing Ideals Of Affine Sets Parameterized By Odd Cycles},
  author = {Miguel Eduardo Uribe Paczka and Eliseo Sarmiento and Carlos Rentería Márquez},
  journal= {arXiv preprint arXiv:1710.11314},
  year   = {2017}
}

Comments

19 pages

R2 v1 2026-06-22T22:30:46.516Z