On the type of an almost Gorenstein monomial curve

Moscariello, Alessio

doi:10.1016/j.jalgebra.2016.02.019

Cited by 22 publications

(21 citation statements)

References 13 publications

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“…In particular, if H is almost symmetric then µ(I) ≤ µ(in(I)) ≤ 7.Proof Applying Theorem 1.1 and the formula (1) for d = 4 , we have the first claim. For the second claim, since H is almost symmetric we have by[15] that t(H) ⩽ 3 and now applying the first claim we get the result.2 Now we investigate the condition (*) in the cases of 4 variables.…”

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confidence: 87%

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On the type and generators of monomial curves

Dung¹

2018

Turk J Math

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Let n1, n2,. .. , n d be positive integers and H be the numerical semigroup generated by n1, n2,. .. , n d. Let A := k[H] := k[t n 1 , t n 2 ,. .. , t n d ] ∼ = k[x1, x2,. .. , x d ]/I be the numerical semigroup ring of H over k. In this paper we give a condition (*) that implies that the minimal number of generators of the defining ideal I is bounded explicitly by its type. As a consequence for semigroups with d = 4 satisfying the condition (*) we have µ(in(I)) ≤ 2(t(H)) + 1 .

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confidence: 87%

“…Moscariello in [15] proved that if H is pseudo-symmetric then its type is at most 3 . More recently, Eto in [9] classified almost symmetric semigroups and gave minimal generators as well as free resolutions for the toric ideal.…”

Section: Introductionmentioning

confidence: 99%

On the type and generators of monomial curves

Dung¹

2018

Turk J Math

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“…Moscariello proves [Mo,Lemma 6] that if H is almost symmetric and e = 4, and if for some j and a ij = 0 for every i = j, then f = F(H)/2. His result can be slightly improved.…”

Section: Fundamental Propertiesmentioning

confidence: 99%

Almost symmetric numerical semigroups

Herzog

Watanabe

2019

Semigroup Forum

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We study almost symmetric numerical semigroups and semigroup rings. We describe a characteristic property of the minimal free resolution of the semigroup ring of an almost symmetric numerical semigroup. For almost symmetric semigroups generated by 4 elements we will give a structure theorem by using the "row-factorization matrices", introduced by Moscariello. As a result, we give a simpler proof of Komeda's structure theorem of pseudo-symmetric numerical semigroups generated by 4 elements. Row-factorization matrices are also used to study shifted families of numerical semigroups.

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“…The notion of an RF-matrix associated to a pseudo-Frobenius number α ∈ PF(H) was introduced by A. Moscariello [11] in 2016, and by means of RF-matrices, Moscariello proved that the Cohen-Macaulay type t(H) of any 4-generated numerical semigroup H is at most 3, if the semigroup ring k[H] over a filed k is an almost Gorenstein graded ring. Because RF-matrices play a very important role in the present paper, let us recall here the definition of RF-matrices also.…”

Section: Rf-matrices Associated To Pseudo-frobenius Numbersmentioning

confidence: 99%