Browsing by Subject "Monomial curve"

Now showing 1 - 6 of 6

Open Access
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.
Open Access
Cohen-macaulayness of tangent cones
(2000) Arslan, Feza
We give a criterion for checking the Cohen-Macaulayness of the tangent cone of a monomial curve by using the Gröbner basis. For a family of monomial curves, we give the full description of the defining ideal of the curve and its tangent cone at the origin. By using this family of curves and their extended versions to higher dimensions, we prove that the minimal number of generators of a Cohen-Macaulay tangent cone of a monomial curve in an affine l-space can be arbitrarily large for l ≥ 4 contrary to the l = 3 case shown by Robbiano and Valla. We also determine the Hubert series of the associated graded ring of this family of curves and their extended versions.
Open Access
Complete intersection monomial curves and the Cohen—Macaulayness of their tangent cones
(World Scientific Publishing, 2019) Katsabekis, Anargyros
Let C(n) be a complete intersection monomial curve in the 4-dimensional affine space. In this paper we study the complete intersection property of the monomial curve C(n + wv), where w > 0 is an integer and v ∈ ℕ4. In addition, we investigate the Cohen–Macaulayness of the tangent cone of C(n + wv).
Open Access
On pseudo symmetric monomial curves
(Taylor & Francis, 2018) Şahin, M.; Şahin, Nil
We study monomial curves, toric ideals and monomial algebras associated to 4-generated pseudo symmetric numerical semigroups. Namely, we determine indispensable binomials of these toric ideals, give a characterization for these monomial algebras to have strongly indispensable minimal graded free resolutions. We also characterize when the tangent cones of these monomial curves at the origin are Cohen–Macaulay.
Open Access
On the Cohen–Macaulayness of tangent cones of monomial curves in A 4 (K)
(TÜBİTAK, 2019-05) Arslan, F.; Katsabekis, Anargyros; Nalbandıyan, M.
In this paper we give necessary and sufficient conditions for the Cohen–Macaulayness of the tangent cone of a monomial curve in 4-dimensional affine space. We particularly study the case where C is a Gorenstein noncomplete intersection monomial curve and we generalize some results in the literature. Moreover, by using these results, we construct families supporting Rossi’s conjecture, which is still open for monomial curves in 4-dimensional affine space.
Open 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.