Criterion for Complete Intersection of certain Monomial Curves

Abstract

Let k be a field and m₀, …, m_e−1 (e ≥ 3) be a sequence of positive integers with gcd(m₀, …, m_e−1) = 1. Let $\mathcal{C}$ be the affine monomial curve in the e-space $\mathbb{A}_{k}^{e}$ defined parametrically by ${T^{{m_0}}}, \ldots ,{X_{e - 1}} = {T^{{m_{e - 1}}}}$. In this article, we assume that m₀, …, m_e−1 form a minimal arithmetic sequence and find some criterion for complete intersection of C.