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arXiv · 1711.11149

On the multiplicity of tangent cones of monomial curves

Alessio Sammartano
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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.

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Alessio Sammartano. 2017-11-29. On the multiplicity of tangent cones of monomial curves. https://doi.org/10.4310/arkiv.2019.v57.n1.a11

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