# Minimal free resolution of the associated graded ring of certain monomial curves

## TL;DR

This paper explicitly computes the minimal free resolution and Hilbert function of the tangent cone for specific affine monomial curves in four-dimensional space, enhancing understanding of their algebraic structure.

## Contribution

It provides the first explicit minimal free resolution and Hilbert function for the tangent cone of certain affine monomial curves in affine 4-space.

## Key findings

- Explicit minimal free resolution of the associated graded ring
- Computed Hilbert function of the tangent cone
- Enhanced understanding of algebraic structure of these curves

## Abstract

In this article, we give the explicit minimal free resolution of the associated graded ring of certain affine monomial curves in affine 4-space based on the standard basis theory. As a result, we give the minimal graded free resolution and compute the Hilbert function of the tangent cone of these families.