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arXiv · 1911.07483

4-Generated Pseudo Symmetric Monomial Curves with not Cohen-Macaulay Tangent Cones

Nil Şahin
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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, non-decreasingness 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 $k(\alpha_2+1)<(k-1)\alpha_1+(k+1)\alpha_{21}+\alpha_3$ is $1$, it is proved that the Hilbert function of the local ring is non-decreasing.

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Nil Şahin. 2019-11-18. 4-Generated Pseudo Symmetric Monomial Curves with not Cohen-Macaulay Tangent Cones. https://doi.org/10.3906/mat-1910-92

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