Related papers: Extremal Betti numbers of graded modules

For any $\ell > 0$, we present an algorithm which takes as input a semi-algebraic set, $S$, defined by $P_1 \leq 0,...,P_s \leq 0$, where each $P_i \in \R[X_1,...,X_k]$ has degree $\leq 2,$ and computes the top $\ell$ Betti numbers of $S$,…

This work concerns finite free complexes with finite length homology over a commutative noetherian local ring $R$. The focus is on complexes that have length $\mathrm{dim}\, R$, which is the smallest possible value, and in particular on…

Let $R$ be a Cohen-Macaulay local ring possessing a canonical module. We compare the initial and terminal Betti numbers of modules in a series of nontrivial cases. We pay special attention to the Betti numbers of the canonical module. Also,…

We give explicit formulas for the Betti numbers, both stable and unstable, of the unordered configuration spaces of an arbitrary surface of finite type.

Let $S$ be a multigraded polynomial ring such that the degree of each variable is a unit vector; so $S$ is the homogeneous coordinate ring of a product of projective spaces. In this setting, we characterize the formal Laurent series which…

For the algebra L= K <x, d/dx, \int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an…

Let S be a polynomial ring over a field of characteristic zero in finitely may variables. Let T be an unramified, finitely generated extension of S with $T^\times = k^\times$. Then T = S.

We obtain tight bounds for the minimal number of generators of an ideal with bounded-degree generators in a polynomial ring $K[X_1,\dots,X_n],$ as well as a sharp quantification of the maximum possible size of a minimal generating set of…

We study the problem of maximizing Betti numbers of simplicial complexes. We prove an upper bound of 1.32^n for the sum of Betti numbers of any n-vertex flag complex and 1.25^n for the independence complex of a triangle-free graph. These…

We give a formula to compute all the top degree graded Betti numbers of the path ideal of a cycle. Also we will find a criterion to determine when Betti numbers of this ideal are non zero and give a formula to compute its projective…

A numerical semigroup $S$ is an additive subsemigroup of the non-negative integers with finite complement, and the squarefree divisor complex of an element $m \in S$ is a simplicial complex $\Delta_m$ that arises in the study of multigraded…

The deviations of a graded algebra are a sequence of integers that determine the Poincare series of its residue field and arise as the number of generators of certain DG algebras. In a sense, deviations measure how far a ring is from being…

The supremum of reduction numbers of ideals having principal reductions is expressed in terms of the integral degree, a new invariant of the ring, which is finite provided the ring has finite integral closure. As a consequence, one obtains…

Finite group actions on free resolutions and modules arise naturally in many interesting examples. Understanding these actions amounts to describing the terms of a free resolution or the graded components of a module as group…

We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial P(T) modulo l. As an application we find the proportion of isogeny classes of abelian varieties with a…

Let $S$ be a semiring. An $S$-semimodule $M$ is called a multiplication semimodule if for each subsemimodule $N$ of $M$ there exists an ideal $I$ of $S$ such that $N=IM$. In this paper we investigate some properties of multiplication…

We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic.

We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.

We describe the cone of Betti tables of all finitely generated graded modules over the homogeneous coordinate ring of three non-collinear points in the projective plane. We also describe the cone of Betti tables of all finite length…

Over the past three decades, there have been several attempts to characterize modules over affine Lie superalgebras. One of the main issues in this regard is dealing with zero-level modules. In this paper, we study these modules and…