On the multiplicity of tangent cones of monomial curves

Abstract

Let Λ be a numerical semigroup, C ⊆ A n the monomial curve singularity associated to Λ, and T its tangent cone. In this paper we provide a sharp upper bound for the least positive integer in Λ in terms of the codimension and the maximum degree of the equations of T , when T is not a complete intersection. A special case of this result settles a question of J. Herzog and D. Stamate.