We study the minimal free resolution of the tangent cone of Gorenstein monomial curves in affine 4-space. We give the explicit minimal free resolution of the tangent cone of noncomplete intersection Gorenstein monomial curve whose tangent cone has five minimal generators and show that the possible Betti sequences are (1, 5, 6, 2) and (1, 5, 5, 1). Moreover, we compute the Hilbert function of the tangent cone of these families as a result.
In this article, even if it is known for general case in [17], we give the explicit minimal free resolution of the associated graded ring of certain a¢ ne monomial curves in a¢ ne 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 A 4 in the simple form according to [17].
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