Browsing by Subject "Standard bases"

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    4-generated pseudo symmetric monomial curves with not Cohen–Macaulay tangent cones
    (TUBITAK, 2020) Şahin, Nil
    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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    ItemOpen Access
    On the Hilbert series of the tangent cones for some 4-generated pseudosymmetric monomial curves
    (TÜBİTAK, 2023-01-01) Şahin, Nil
    In this article, we study Hilbert series of non-Cohen-Maculay tangent cones for some 4-generated pseudosymmetric monomial curves. We show that the Hilbert function is nondecreasing by explicitly computing it. We also compute standard bases of these toric ideals.