Related papers: Algorithms for graded injective resolutions and lo…

In this paper we study the local cohomology of all finitely generated bigraded modules over a standard bigraded polynomial ring which have only one nonvanishing local cohomology with respect to one of the irrelevant bigraded ideals.

Let $R=\Bbbk[x_1,\..., x_n]$ and $M=R^s/I$ a multigraded squarefree module. We discuss the construction of cochain complexes associated to $M$ and we show how to interpret homological invariants of $M$ in terms of topological computations.…

Let $R$ be a polynomial or power series ring over a field $k$. We study the length of local cohomology modules $H^j_I(R)$ in the category of $D$-modules and $F$-modules. We show that the $D$-module length of $H^j_I(R)$ is bounded by a…

The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived…

Considering finite extensions K[A] \subseteq K[B] of positive affine semigroup rings over a field K we have developed in [1] an algorithm to decompose K[B] as a direct sum of monomial ideals in K[A]. By computing the regularity of…

We consider the (graded) Matlis dual $\DD(M)$ of a graded $\D$-module $M$ over the polynomial ring $R = k[x_1, \ldots, x_n]$ ($k$ is a field of characteristic zero), and show that it can be given a structure of $\D$-module in such a way…

Let $S=k[x_1,..., x_n]$ be a polynomial ring over a field $k$ with $n$ variables $x_1$, ..., $x_n$, $\mmmm$ the irrelevant maximal ideal of $S$, $I$ a monomial ideal in $S$ and $I'$ the polarization of $I$ in the polynomial ring $S'$ with…

This article is a sequel to hep-th/9411050, q-alg/9412017, q-alg/9503013. Given a collection of $m$ finite factorizable sheaves $\{\CX_k\}$, we construct here some perverse sheaves over configuration spaces of points on a projective line…

Let $(R, \frak m)$ be a homomorphic image of a Cohen-Macaulay local ring and $M$ a finitely generated $R$-module. We use the splitting of local cohomology to shed a new light on the structure of non-Cohen-Macaulay modules. Namely, we show…

In this paper, we construct an explicit minimal projective bimodule resolution of a self-injective special biserial algebra $A_{T}$ ($T\geq0$) whose Grothendieck group is of rank $4$. As a main result, we determine the dimension of the…

Let $(A,\mathfrak{m})$ be a Gorenstein local ring and let $M$ be a finitely generated Cohen Macaulay $A$ module. Let $G(A)=\bigoplus_{n\geq 0}\mathfrak{m}^n/\mathfrak{m}^{n+1}$ be the associated graded ring of $A$ and $G(M)=\bigoplus_{n\geq…

Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology of it. In the literature, there exist various algorithms for computing the homology groups of simplicial complexes…

Let $R$ be a standard graded, finitely generated algebra over a field, and let $M$ be a graded module over $R$ with all Bass numbers finite. Set $(-)^{(n)}$ to be the $n$-th Veronese functor. We compute the Bass numbers of $M^{(n)}$ over…

In this paper, we construct a local ring $A$ such that the kernel of the map $G_0(A)\subq \to G_0(\hat{A})\subq$ is not zero, where $\hat{A}$ is the comletion of $A$ with respect to the maximal ideal, and $G_0()\subq$ is the Grothendieck…

We investigate the finiteness of the set of associated primes for local cohomology modules $H_I^{i}(J)$ of an ideal $J$ generated by an $R$-sequence, through the comparison of $H_I^{d+1}(J)$ and $H_I^d(R/J)$, where $d =…

We characterize the class of ideals of a polynomial ring such that the hilbert series of their graded local cohomology modules is maximal.

This thesis is a study of various ways of measuring the size and complexity of finitely generated modules over a Noetherian local ring. The classical example is the multiplicity or degree. Here we investigate several variants of the degree…

The aim of this paper is to obtain a uniform bound for a certain class of submodules from the following theorem: Let $(R,\frak m)$ be a local ring, let $M$ be a finite $R$--module of dimension $d\ge 1$ and let $\frak q$ be an ideal of $R$…

Let $G$ be the group scheme $\operatorname{SL}_{d+1}$ over $\mathbb{Z}$ and let $Q$ be the parabolic subgroup scheme corresponding to the simple roots $\alpha_{2},\cdots,\alpha_{d-1}$. Then $G/Q$ is the $\mathbb{Z} $-scheme of partial flags…

This paper addresses the problem of decomposing a numerical semigroup into m-irreducible numerical semigroups. The problem originally stated in algebraic terms is translated, introducing the so called Kunz-coordinates, to resolve a series…