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Tangent cones of monomial curves obtained by numerical duplication

  • Autores: Marco D'Anna, Raheleh Jafari, Francesco Strazzanti
  • Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 70, Fasc. 3, 2019, págs. 461-477
  • Idioma: inglés
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • Given a numerical semigroup ring ?=?⟦?⟧ , an ideal E of S and an odd element ?∈? , the numerical duplication ?⋈?? is a numerical semigroup, whose associated ring ?⟦?⋈??⟧ shares many properties with the Nagata’s idealization and the amalgamated duplication of R along the monomial ideal ?=(??∣?∈?) . 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 gr?(?) is Cohen–Macaulay and when gr?(??) is a canonical module of gr?(?) in terms of numerical semigroup’s properties, where ?? is a canonical module of R.


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