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On the multiplicity of tangent cones of monomial curves

Alessio Sammartano University of Notre Dame

Algebraic Geometry mathscidoc:1912.43036

Arkiv for Matematik, 57, (1), 214-225, 2019
Let Λ be a numerical semigroup, C⊆An 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.
multiplicity, degree, associated graded ring, tangent cone, monomial curve, numerical semigroup, Betti numbers, initial ideal
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@inproceedings{alessio2019on,
  title={On the multiplicity of tangent cones of monomial curves},
  author={Alessio Sammartano},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204134451768442592},
  booktitle={Arkiv for Matematik},
  volume={57},
  number={1},
  pages={214-225},
  year={2019},
}
Alessio Sammartano. On the multiplicity of tangent cones of monomial curves. 2019. Vol. 57. In Arkiv for Matematik. pp.214-225. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204134451768442592.
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