Related papers: Normal Hilbert Polynomials : A survey

Principal symmetric ideals were recently introduced by Harada, Seceleanu, and Sega, with a focus on their homological properties. They are ideals generated by the orbit of a single polynomial under permutations of variables in a polynomial…

Let $R$ be a commutative Noetherian ring that is a smooth $\mathbb Z$-algebra. For each ideal $I$ of $R$ and integer $k$, we prove that the local cohomology module $H^k_I(R)$ has finitely many associated prime ideals. This settles a crucial…

Macaulay's theorem and Fr\"oberg's conjecture deal with the Hilbert function of homogeneous ideals in polynomial rings $S$ over a field $K$. In this short note we present some questions related to variants of Macaulay's theorem and…

We propose a general study of standard bases of polynomial ideals with parameters in the case where the monomial order is arbitrary. We give an application to the computation of the stratification by the local Hilbert-Samuel function.…

Let $D$ be an integrally closed local Noetherian domain of Krull dimension 2, and let $f$ be a nonzero element of $D$ such that $fD$ has prime radical. We consider when an integrally closed ring $H$ between $D$ and $D_f$ is determined…

We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are…

The Sally module of an ideal is an important tool to interplay between Hilbert coefficients and the properties of the associated graded ring. In this paper we give new insights on the structure of the Sally module. We apply these results…

In this paper we study classes of monomial ideals for which all of its powers have a linear resolution. Let K[x_{1},x_{2}] be the polynomial ring in two variables over the field K, and let L be the generalized mixed product ideal induced by…

In this paper, we obtain explicit formulas for the Hilbert series and Hilbert depth of squarefree Veronese ideals in a standard graded polynomial ring.

In the paper we give an upper bound for the Waldschmidt constants of the wide class of ideals. This generalizes the result obtained by Dumnicki, Harbourne, Szemberg and Tutaj-Gasinska, Adv. Math. 2014. Our bound is given by a root of a…

Using results obtained from the study of homogeneous ideals sharing the same initial ideal with respect to some term order, we prove the singularity of the point corresponding to a segment ideal with respect to the revlex term order in the…

Let $I$ and $J$ be two ideals of a commutative Noetherian ring $R$ and $M$ be an $R$-module of dimension $d$. If $R$ is a complete local ring and $M$ is finite, then attached prime ideals of $H^{d-1}_{I,J}(M)$ are computed by means of the…

We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal…

Let $p$ be a prime number, $\Bbbk$ a field of characteristic $p$ and $G$ a finite $p$-group. Let $V$ be a finite-dimensional linear representation of $G$ over $\Bbbk$. Write $S = \mathrm{Sym} V^*$. For a class of $p$-groups which we call…

Scattered over the past few years have been several occurrences of simplicial complexes whose topological behavior characterize the Cohen-Macaulay property for quotients of polynomial rings by arbitrary (not necessarily squarefree) monomial…

Let S=K[x_1,...,x_n] be a polynomial ring. Denote by $p_a$ the power sum symmetric polynomial x_1^a+...+x_n^a. We consider the following two questions: Describe the subsets $A \subset \mathbb{N}$ such that the set of polynomials $p_a$ with…

Let $G$ be a simple graph on $n$ vertices and let $J_{G,m}$ be the generalized binomial edge ideal associated to $G$ in the polynomial ring $K[x_{ij}, 1\le i \le m, 1\le j \le n]$. We classify the Cohen-Macaulay generalized binomial edge…

To a simplicial complex, we associate a square-free monomial ideal in the polynomial ring generated by its vertex set over a field. We study algebraic properties of this ideal via combinatorial properties of the simplicial complex. By…

Monomial ideals and toric rings are closely related. By consider a Grobner basis we can always associated to any ideal $I$ in a polynomial ring a monomial ideal ${\rm in}_\prec I$, in some special situations the monomial ideal ${\rm…

Let S be a finitely generated standard multi-graded algebra over a Noetherian local ring A. This paper first expresses mixed multiplicities of S in term of Hilbert-Samuel multiplicity that explained the mixed multiplicities S as the…