Related papers: Normal Hilbert Polynomials : A survey

In this paper, we obtain a generalization, in dimension $3$, of a theorem of David Rees about joint reductions of the bigraded filtration $\{ \overline{I^rJ^s}\}$ of complete ${\mathfrak m}$-primary ideals and vanishing of the second normal…

In a recent paper by Harada, Seceleanu, and \c{S}ega, the Hilbert function, betti table, and graded minimal free resolution of a general principal symmetric ideal are determined when the number of variables in the polynomial ring is…

We characterise ideals in two-dimensional regular local rings that arise as ideals of maximal minors of indecomposable integrally closed modules of rank two.

Let $(R,\mathfrak{m},k)$ denote a local ring. For $I$ and $J$ ideals of $R$, for all integer $i$, let $H^i_{I,J}(-)$ denote the $i$-th local cohomology functor with respect to $(I,J)$. Here we give a generalized version of Local Duality…

Let $A = K[x_1, ..., x_n]$ denote the polynomial ring in $n$ variables over a field $K$. We will classify all the Gotzmann ideals of $A$ with at most $n$ generators. In addition, we will study Hilbert functions $H$ for which all homogeneous…

Let Hilb^p be the Hilbert scheme parametrizing the closed subschemes of P^n with Hilbert polynomial p \in Q[t] over a field K of characteristic zero. By bounding below the cohomological Hilbert functions of the points of Hilb^p we define…

Let $(R, \mathfrak m)$ denote an $n$-dimensional Gorenstein ring. For an ideal $I \subset R$ of height $c$ we are interested in the endomorphism ring $B = \Hom_R(H^c_I(R), H^c_I(R)).$ It turns out that $B$ is a commutative ring. In the case…

Let I be a homogeneous ideal in a polynomial ring P over a field. By Macaulay's Theorem, there exists a lexicographic ideal L=Lex(I) with the same Hilbert function as I. Peeva has proved that the Betti numbers of P/I can be obtained from…

Using linear algebra methods we study certain algebraic properties of monomial rings and matroids. Let I be a monomial ideal in a polynomial ring over an arbitrary field. If the Rees cone of I is quasi-ideal, we express the normalization of…

Abhyankar defined an ideal to be Hilbertian if its Hilbert polynomial coincides with its Hilbert function for all nonnegative integers. In 1984, he proved that the ideal of (r+1)-order minors of a generic p x q matrix is Hilbertian. We give…

We give an explicit formula for the Hilbert-Poincar\'{e} series of the parity binomial edge ideal of a complete graph $K_{n}$ or equivalently for the ideal generated by all $2\times 2$-permanents of a $2\times n$-matrix. It follows that the…

The authors introduced the notion of $p_g$-ideals for two-dimensional excellent normal local domain over an algebraicaly closed field in terms of resolution of singularities. In this note, we give several ring-theoretic characterization of…

This work reports and classifies the most general construction of rational quantum potentials in terms of the generalized Hermite polynomials. This is achieved by exploiting the intrinsic relation between third-order shape-invariant…

For positive integers m >= n >= p, we compute the GL_m x GL_n-equivariant description of the local cohomology modules of the polynomial ring S of functions on the space of m x n matrices, with support in the ideal of p x p minors. Our…

Students studying the Lasker-Noether theorem on primary decomposition of ideals may want to see an example of an ideal (necessarily in a non-Noetherian ring) which does not have a primary decomposition. The most well-known counterexample is…

The structure of Sally modules of $\fkm$-primary ideals $I$ in a Cohen-Macaulay local ring $(A, \m)$ satisfying the equality $\e_1(I)=\e_0(I)-\ell_A(A/I)+1$ is explored, where $\e_0(I)$ and $\e_1(I)$ denote the first two Hilbert…

We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and…

We construct a generalize Ishida complex to compute the local cohomology with monomial support of modules over quotients of polynomial rings by cellular binomial ideals. As a consequence, we obtain a combinatorial criterion to determine…

In the present paper we investigate a question stemming from a long-standing conjecture of Vasconcelos: given a generically a complete intersection perfect ideal I in a regular local ring R, is it true that if I/I^2 (or R/I^2) is…

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see,…