Hilbert series of tangent cones for Gorenstein monomial curves in A4(K)

Abstract

In this paper, we study the Hilbert series of the tangent cone of Gorenstein monomial curves in the 4- dimensional affine space. We give an explicit formula for the reduced Hilbert series of the tangent cone of a noncomplete intersection Gorenstein monomial curve whose tangent cone is Cohen–Macaulay.