Tangent Cone of Numerical Semigroup Rings of Embedding Dimension Three

Yi-Huang Shen

Tangent Cone of Numerical Semigroup Rings of Embedding Dimension Three

Commutative Algebra 2011-06-23 v2

Authors: Yi-Huang Shen

Abstract

In this paper, we give new characterizations of the Buchsbaum and Cohen-Macaulay properties of the tangent cone $\gr_\frakm(R)$ , where $(R,\frakm)$ is a numerical semigroup ring of embedding dimension 3. In particular, we confirm the conjectures raised by Sapko on the Buchsbaumness of $\gr_\frakm(R)$ .

Keywords

tangent cone numerical semigroup ring embedding dimension three Buchsbaum property Cohen-Macaulay property conjecture confirmation

Cite

@article{arxiv.0808.2162,
  title  = {Tangent Cone of Numerical Semigroup Rings of Embedding Dimension Three},
  author = {Yi-Huang Shen},
  journal= {arXiv preprint arXiv:0808.2162},
  year   = {2011}
}

Comments

18 pages. Title is modified and discussion of embedding dimension 4 case is dropped. Accepted to the Communications in Algebra

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