A variation of gluing of numerical semigroups

Numata, Takahiro

doi:10.1007/s00233-015-9760-y

Cited by 7 publications

(5 citation statements)

References 8 publications

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“…The next result is a nice consequence of Propositions 3.1 and 3.2 and it was proved by Numata [19] in the almost symmetric case.…”

Section: Gluing and Generalized Arithmetic Sequencessupporting

confidence: 54%

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Nearly Gorenstein vs almost Gorenstein affine monomial curves

Moscariello¹,

Strazzanti²

2020

Preprint

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We extend some results on almost Gorenstein affine monomial curves to the nearly Gorenstein case. In particular, we prove that the Cohen-Macaulay type of a nearly Gorenstein monomial curve in A 4 is at most 3, answering a question of Stamate in this particular case. Moreover, we prove that, if C is a nearly Gorenstein affine monomial curve which is not Gorenstein and n1, . . . , nν are the minimal generators of the associated numerical semigroup, the elements of {n1, . . . , ni, . . . , nν } are relatively coprime for every i.

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“…The next result is a nice consequence of Propositions 3.1 and 3.2 and it was proved by Numata [19] in the almost symmetric case.…”

Section: Gluing and Generalized Arithmetic Sequencessupporting

confidence: 54%

“…, dn ν−1 , n ν . The numerical semigroup T is symmetric if and only if S is symmetric, see [8,Proposition 8], whereas Numata [19] proved that T is never almost symmetric when S is not symmetric. In the next proposition we show that this result holds also for the nearly Gorenstein property.…”

Section: Gluing and Generalized Arithmetic Sequencesmentioning

confidence: 99%

Nearly Gorenstein vs almost Gorenstein affine monomial curves

Moscariello¹,

Strazzanti²

2020

Preprint

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“…The Betti numbers of K[H] when H is a numerical semigroup obtained by gluing have also been considered in [34] and [56].…”

Section: Betti Numbers For Simple Gluingsmentioning

confidence: 99%

Betti numbers for numerical semigroup rings

Stamate

2018

Preprint

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“…As indicated in [14], a minimal S k -graded free resolution of K[S k ] is obtained from a minimal S-graded free resolution of K[S] via the faithfully flat extension f : R → R, defined by sending x 1 → x k 1 and x i → x i for all i > 1. These prove the following Proposition 4.1.…”

Section: Minimal Free Resolutionsmentioning

confidence: 99%

Liftings of a Monomial Curve

Şahin

2018

Bull. Aust. Math. Soc.

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We study an operation, that we call lifting, creating nonisomorphic monomial curves from a single monomial curve. Our main result says that all but finitely many liftings of a monomial curve have Cohen–Macaulay tangent cones even if the tangent cone of the original curve is not Cohen–Macaulay. This implies that the Betti sequence of the tangent cone is eventually constant under this operation. Moreover, all liftings have Cohen–Macaulay tangent cones when the original monomial curve has a Cohen–Macaulay tangent cone. In this case, all the Betti sequences are just the Betti sequence of the original curve.

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A variation of gluing of numerical semigroups

Cited by 7 publications

References 8 publications

Nearly Gorenstein vs almost Gorenstein affine monomial curves

Nearly Gorenstein vs almost Gorenstein affine monomial curves

Betti numbers for numerical semigroup rings

Liftings of a Monomial Curve

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