Minimal Systems of Binomial Generators for the Ideals of Certain Monomial Curves

Abstract

Let a,b and n>1 be three positive integers such that a and ∑j=0n−1bj are relatively prime. In this paper, we prove that the toric ideal I associated to the submonoid of N generated by {∑j=0n−1bj}∪{∑j=0n−1bj+a∑j=0i−2bj∣i=2,…,n} is determinantal. Moreover, we prove that for n>3, the ideal I has a unique minimal system of generators if and only if ab−1.

Keywords

• binomial ideal
• semigroup ideal
• minimal system of generators
• determinantal ideal
• Gröbner basis
• indispensability