The aim of the article is to study the Betti numbers of the tangent cone of Gorenstein monomial curves in affine 4-space. If $C_S$ is a noncomplete intersection Gorenstein monomial curve whose tangent cone is Cohen--Macaulay, we show that the possible Betti sequences are (1,5,5,1), (1,5,6,2) and (1,6,8,3).
"On the Betti numbers of the tangent cones for Gorenstein monomial curves,"
Turkish Journal of Mathematics: Vol. 45:
6, Article 15.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss6/15