A Gröbner Basis for Certain Affine Monomial Curves

Abstract

Let K be a field and let m ₀,…, m _e−1 be a sequence of positive integers. Let 𝒞 be a monomial curve in the affine e-space , defined parametrically by X ₀ = T ^{m ₀} ,…, X _e−1 = T ^{m _e−1} and let 𝔭 be the defining ideal of 𝒞. In this article, we assume that some e − 1 terms of m ₀,…, m _e−1 form an arithmetic sequence and produce a Gröbner basis for 𝔭.

Key Words:

• Monomial curves
• Gröbner basis

Acknowledgments

The author thanks Professors D. P. Patil, J. Stückrad, and J. Apel for some useful discussions and comments. During this work the author was a CSIR Senior Research Fellow.