Betti numbers for certain Cohen-Macaulay tangent cones

Abstract

In this article, we compute Betti numbers for a Cohen-Macaulay tangent cone of a monomial curve in the affine $4$-space corresponding to a pseudo symmetric numerical semigroup. As a byproduct, we also show that for these semigroups, being of homogeneous type and homogeneous are equivalent properties.

Bull. Aust. Math. Soc. published online