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Paper   IPM / M / 15511
School of Mathematics
  Title:   Tangent cones of monomial curves obtained by numerical duplication
  Author(s):  Raheleh Jafari (Joint with M. D'Anna amd F. Strazzanti)
  Status:   Published
  Journal: Collect. Math.
  Year:  2019
  Pages:   DOI: 10.1007/s13348-019-00241-w
  Supported by:  IPM
Given a numerical semigroup ring R=k[[S]], an ideal E of S and an odd element b∈S, the numerical duplication S⋈bE is a numerical semigroup, whose associated ring k[[S⋈bE]] shares many properties with the Nagata's idealization and the amalgamated duplication of R along the monomial ideal I=(te∣e∈E). In this paper we study the associated graded ring of the numerical duplication characterizing when it is Cohen-Macaulay, Gorenstein or complete intersection. We also study when it is a homogeneous numerical semigroup, a property that is related to the fact that a ring has the same Betti numbers of its associated graded ring. On the way we also characterize when grm(I) is Cohen-Macaulay and when grm(ωR) is a canonical module of grm(R) in terms of numerical semigroup's properties, where ωR is a canonical module of R.

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