Related papers: Regularity and algebraic properties of certain lat…
In this paper, we recover the characteristic polynomial of an arrangement of hyperplanes by computing the rational equivalence class of the variety defined by the logarithmic ideal of the arrangement. The logarithmic ideal was introduced in…
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…
We generalize some properties related to Hilbert series and Lefschetz properties of Milnor algebras of projective hypersurfaces with isolated singularities to the more general case of an almost complete intersection ideal $J$ of dimension…
We consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the variables. In previous work, we determined the possible…
The notion of regularity has been used by S. Kleiman in the construction of bounded families of ideals or sheaves with given Hilbert polynomial, a crucial point in the construction of Hilbert or Picard scheme. In a related direction,…
In this paper, we investigate the structure of the saturation of ideals generated by sparse homogeneous polynomials over a projective toric variety $X$ with respect to the irrelevant ideal of $X$. As our main results, we establish a duality…
We obtain an improved lower bound for the regularity of the binomial edge ideals of trees. We prove an upper bound for the regularity of the binomial edge ideals of certain subclass of block-graphs. As a consequence we obtain sharp upper…
When M is a finitely generated graded module over a standard graded algebra S and I is an ideal of S, it is known from work of Cutkosky, Herzog, Kodiyalam, R\"omer, Trung and Wang that the Castelnuovo-Mumford regularity of I^mM has the form…
We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we…
We investigate the standard graded $k$-algebras over a field $k$ of characteristic zero for which general linear forms are exact zero divisors. We formulate a conjecture regarding the Hilbert function of such rings. We prove our conjecture…
Let $X \subset {\mathbb R}^m$ be a spherical code (i.e., a finite subset of the unit sphere) and consider the ideal of all polynomials in $m$ variables which vanish on $X$. Motivated by a study of cometric ($Q$-polynomial) association…
In this paper we study the normality of monomial ideals using linear programming and graph theory. We give normality criteria for monomial ideals, for ideals generated by monomials of degree two, and for edge ideals of graphs and clutters…
In this paper we study homological properties of the Rees ring R of the graded maximal ideal of a standard graded k-algebra A. In particular we are interested the comparison of the depth and regularity of A and R.
We find a class of block graphs whose binomial edge ideals have minimal regularity. As a consequence, we characterize the trees whose binomial edge ideals have minimal regularity. Also, we show that the binomial edge ideal of a block graph…
We study homological properties of random quadratic monomial ideals in a polynomial ring $R = {\mathbb K}[x_1, \dots x_n]$, utilizing methods from the Erd\"{o}s-R\'{e}nyi model of random graphs. Here for a graph $G \sim G(n, p)$ we consider…
We introduce a persistent commutative algebra for studying the algebraic and combinatorial evolution of edge ideals of graphs and hypergraphs under filtration. Building on the Persistent Stanley--Reisner Theory (PSRT), we develop the notion…
Let R=K[M] be a normal affine monoid algbera over a field K.Up to isomorphism the conic ideals are exactly the direct summands ofthe extension R^{1/n} of R. We show that the classes of the conic divisorial ideals can be identified with the…
Let $E$ be an arbitrary (countable) graph and let $R$ be a unital commutative ring. We analyze the ideal structure of the Leavitt path algebra $\lr$ introduced by Mark Tomforde. We first modify the definition of basic ideals and we then…
We study the set of algebraic objects known as vanishing polynomials (the set of polynomials that annihilate all elements of a ring) over general commutative rings with identity. These objects are of special interest due to their close…
Let $(R,\mathfrak{m},\Bbbk)$ be a regular local ring of dimension 3. Let $I$ be a Gorenstein ideal of $R$ of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric matrix of odd size such that $I$ is generated by the…