On minimal free resolution of the associated graded rings of certain monomial curves : New proofs in A⁴

Abstract

In this article, even if it is known for general case in <cite>sharifan-nahandi</cite>, 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 the Hilbert function of the tangent cone of these families in A⁴ in the simple form according to <cite>sharifan-nahandi</cite>.