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.
📌 3 Key Takeaways
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Objective & Hypothesis: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.
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Key Findings & Data:As the tangent cones are not Cohen-Macaulay, nondecreasingness of the Hilbert function of the local ring was not guaranteed.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
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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Cite This Article
ŞAHİN, N. (2022). 4-generated pseudo symmetric monomial curves with not Cohen–Macaulay tangent cones. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 6, 2174–2184. https://ajindex.com/articles/608781
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