Monomial curve families supporting Rossiʼs conjecture

Arslan, Feza; Sipahi, Neslihan; Şahin, Nil

doi:10.1016/j.jsc.2013.03.002

Cited by 3 publications

(4 citation statements)

References 9 publications

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“…that is a contradiction by (4) . Therefore we can proceed as in the case h = −1, b = 1 treated above when ℓ is odd.…”

mentioning

confidence: 88%

“…• T (4) := T (3) ✶ 669 M(T (3) ) is almost symmetric with type 607 and • T := T (4) ✶ 1373 K, where K := K(T (4) ) + f (T (4) ) + 1 ⊆ T (4) , is symmetric and has Hilbert function Since a symmetric numerical semigroup is almost symmetric the Hilbert functions above can be computed from the one of T 0 by means of Proposition 1.4.…”

Section: The Gorenstein Casementioning

confidence: 99%

“…• In [4] F. Arslan, N. Sipahi and N. Şahin, for other 4-generated Gorenstein numerical semigroup rings constructed by non-nice gluing;…”

Section: Introductionmentioning

confidence: 99%

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One-dimensional Gorenstein local rings with decreasing Hilbert function

2017

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In this paper we solve a problem posed by M.E. Rossi: Is the Hilbert function of a Gorenstein local ring of dimension one not decreasing? More precisely, for any integer h>1, hâ\u88\u8914+22k,35+46k|kâ\u88\u88N, we construct infinitely many one-dimensional Gorenstein local rings, included integral domains, reduced and non-reduced rings, whose Hilbert function decreases at level h; moreover, we prove that there are no bounds to the decrease of the Hilbert function. The key tools are numerical semigroup theory, especially some necessary conditions to obtain decreasing Hilbert functions found by the first and the third author, and a construction developed by V. Barucci, M. D'Anna and the second author, that gives a family of quotients of the Rees algebra. Many examples are included

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“…that is a contradiction by (4) . Therefore we can proceed as in the case h = −1, b = 1 treated above when ℓ is odd.…”

mentioning

confidence: 88%

Section: The Gorenstein Casementioning

confidence: 99%

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One-dimensional Gorenstein local rings with decreasing Hilbert function

2017

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“…The conjecture is open for local rings corresponding to 4-generated symmetric semigroups with α 2 > α 21 + α 24 . For some recent work on the monotonicity of the Hilbert function, see [1][2][3][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

4-generated pseudo symmetric monomial curves with not Cohen–Macaulay tangent cones

Şahin¹

2020

Turk J Math

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In this article, standard bases of some toric ideals associated to 4-generated pseudo symmetric semigroups with not Cohen-Macaulay tangent cones at the origin are computed. As the tangent cones are not Cohen-Macaulay, nondecreasingness of the Hilbert function of the local ring was not guaranteed. Therefore, using these standard bases, Hilbert functions are explicitly computed as a step towards the characterization of Hilbert function. In addition, when the smallest integer satisfying k(α2 + 1) < (k − 1)α1 + (k + 1)α21 + α3 is 1 , it is proved that the Hilbert function of the local ring is nondecreasing.

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