On the multiplicity of tangent cones of monomial curves

Abstract

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

To appear on Arkiv för Matematik

References in corpus (3)

• Quadratic numerical semigroups and the Koszul property
• Consecutive cancellations in Betti numbers of local rings
• Consecutive cancellations in Tor modules over local rings