Tangent cones of monomial curves obtained by numerical duplication

2018/03/22 by D'Anna, Marco, Jafari, Raheleh, Strazzanti, Francesco · 1 citation
#13A30 #13H10 #20M14 #20M25 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.08302

Abstract

Given a numerical semigroup ring R=k[ [S] ], an ideal E of S and an odd element b ∈ S, the numerical duplication S \Join^b E is a numerical semigroup, whose associated ring k[ [S \Join^b E] ] shares many properties with the Nagata's idealization and the amalgamated duplication of R along the monomial ideal I=(t^e | 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 \rm gr_{\mathfrak m}(I) is Cohen-Macaulay and when \rm gr_{\mathfrak m}(ω_R) is a canonical module of \rm gr_{\mathfrak m}(R) in terms of numerical semigroup's properties, where ω_R is a canonical module of R.

Cited by

• On the Ratliff-Rush closure of an ideal of a one-dimensional ring

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