Minimal free resolutions of the tangent cones for Gorenstein monomial curves

Authors: PINAR METE, ESRA EMİNE ZENGİN

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 tangentcone has fiveminimal generators and showthat 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.

Keywords: Gorenstein monomial curves, tangent cones, minimal free resolutions

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