English

Reduced Gr\"obner Bases of Certain Toric Varieties; A New Short Proof

Commutative Algebra 2010-09-07 v1

Abstract

Let K be a field and let m_0,...,m_{n} be an almost arithmetic sequence of positive integers. Let C be a toric variety in the affine (n+1)-space, defined parametrically by x_0=t^{m_0},...,x_{n}=t^{m_{n}}. In this paper we produce a minimal Gr\"obner basis for the toric ideal which is the defining ideal of C and give sufficient and necessary conditions for this basis to be the reduced Gr\"obner basis of C, correcting a previous work of \cite{Sen} and giving a much simpler proof than that of \cite{Ayy}.

Keywords

Cite

@article{arxiv.1009.0790,
  title  = {Reduced Gr\"obner Bases of Certain Toric Varieties; A New Short Proof},
  author = {Ibrahim Al-Ayyoub},
  journal= {arXiv preprint arXiv:1009.0790},
  year   = {2010}
}