Complete intersection monomial curves and the Cohen-Macaulayness of their tangent cones

TL;DR

This paper investigates how shifting parameters affects the complete intersection property and Cohen-Macaulayness of tangent cones of certain monomial curves in four-dimensional space.

Contribution

It introduces conditions under which the complete intersection property and Cohen-Macaulayness are preserved when parameters are shifted in monomial curves.

Findings

Conditions for complete intersection property after parameter shift

Criteria for Cohen-Macaulayness of tangent cones

Behavior of monomial curves under parameter modifications

Abstract

Let $C({\bf n})$ be a complete intersection monomial curve in the 4-dimensional affine space. In this paper we study the complete intersection property of the monomial curve $C({\bf n}+w{\bf v})$, where $w>0$ is an integer and ${\bf v} \in \mathbb{N}^{4}$. Also we investigate the Cohen-Macaulayness of the tangent cone of $C({\bf n}+w{\bf v})$.