Related papers: On monomial curves obtained by gluing
In this article, by using the technique of gluing semigroups, we give infinitely many families of 1-dimensional local rings with non-decreasing Hilbert functions. More significantly, these are local rings whose associated graded rings are…
In this paper our aim is twofold. First, we introduce the notion of star gluing of numerical semigroups and show that arithmetically Cohen-Macaulay and Gorenstein properties of the projective closure are preserved under this gluing…
In this paper we give necessary and sufficient conditions for the Cohen-Macaulayness of the tangent cone of a monomial curve in the 4-dimensional affine space. We study particularly the case where $C$ is a Gorenstein non-complete…
In this paper, we use the Ap\'ery table of the numerical semigroup associated to an affine monomial curve in order to characterize arithmetic properties and invariants of its tangent cone. In particular, we precise the shape of the Ap\'ery…
Let $C$ be a Gorenstein non complete intersection monomial curve in the 4-dimensional affine space. In this paper we study the minimal number of generators of the tangent cone of $C$. Special attention will be paid to the case where $C$ has…
In this article, we study Hilbert Series of non-Cohen-Maculay tangent cones for some 4-generated pseudo symmetric monomial curves. We show that the Hilbert Function is nondecreasing by explicitly computing it. We also compute standard bases…
In this paper, our aim is twofold: First, by using the technique of gluing semigroups, we give infinitely many families of a projective closure with the Cohen-Macaulay (Gorenstein) property. Also, we give an effective technique for…
The main goal of this paper is to study some local and global properties of secant varieties of algebraic curves. These results complement our previous work [8] by addressing issues given therein and providing solutions to problems raised…
We discuss some research problems on affine monomial curves, from the perspective of computation.
We discuss algebraic and homological properties of binomial edge ideals associated to graphs which are obtained by gluing of subgraphs and the formation of cones.
We study an operation, that we call lifting, creating non-isomorphic monomial curves from a single monomial curve. Our main result says that all but finitely many liftings of a monomial curve have Cohen-Macaulay tangent cones even if the…
We introduce a general technique for decomposing monomial algebras which we use to study the Lefschetz properties. We apply our technique to various classes of algebras, including monomial almost complete intersections and Gorenstein…
In this article, we give the explicit minimal free resolution of the associated graded ring of certain affine monomial curves in affine 4-space based on the standard basis theory. As a result, we give the minimal graded free resolution and…
We prove new characterizations based on Gr\"obner bases for the Cohen-Macaulay property of a projective monomial curve.
Let $C({\bf n})$ 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 $C({\bf n}+w{\bf v})$, where $w>0$ is an integer and ${\bf v} \in…
In this paper we study the Hilbert function of $\gr_{\mathfrak{m}}(R)$, when $R$ is a numerical semigroup ring or, equivalently, the coordinate ring of a monomial curve. In particular, we prove a sufficient condition for a numerical…
Let $A \bowtie^{f,g} (J,J')$ be the bi--amalgamation of a commutative ring $A$ with $(B,C)$ along the ideals $(J,J')$ with respect to the ring homomorphisms $(f,g)$. In this article, we study the basic homological properties of the…
In this article, 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…
Properties of the recently reported homogeneous Hilbert curves are deduced and reported. The nature of the affine transformations involved in the construction of the Hilbert curves is explored. The analytical representation of proper and…
We introduce the concept of homogeneous numerical semigroups and show that all homogeneous numerical semigroups with Cohen-Macaulay tangent cones are of homogeneous type. In embedding dimension three, we classify all numerical semigroups of…