Tangent Cone of Numerical Semigroup Rings of Embedding Dimension Three

Details Tangent Cone of Numerical Semigroup Rings of Embedding Dimension Three Tangent Cone of Numerical Semigroup Rings of Embedding Dimension Three

2008-08-15

arxiv.org/abs/0808.2162v2

Mathematics

Commutative Algebra

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

Scientific paper

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
$\gr_\frakm(R)$.

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