Minimal free resolutions of the tangent cones for Gorenstein monomial curves

Abstract

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.