Resumen de Tangent cones of monomial curves obtained by numerical duplication

Marco D'Anna , Raheleh Jafari, Francesco Strazzanti

• 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.