A note on Gorenstein monomial curves

Abstract

Let $k$ be an arbitrary field. In this note, we show that if a sequence of relatively prime positive integers $\mathbf{a}=(a_1,a_2,a_3,a_4)$ defines a Gorenstein non complete intersection monomial curve $\mathcal{C}(\mathbf{a})$ in ${\mathbb{A}}_k^4$, then there exist two vectors $\mathbf{u}$ and $\mathbf{v}$ such that $\mathcal{C}(\mathbf{a}+t\mathbf{u})$ and $\mathcal{C}(\mathbf{a}+t\mathbf{v})$ are also Gorenstein non complete intersection affine monomial curves for almost all $t\ge 0$.

References in corpus (1)

• Periodic Occurance of Complete Intersection Monomial Curves

Cited by in corpus (1)

• On the Cohen-Macaulayness of tangent cones of monomial curves in ${\mathbb{A}}^4(K)$