Related papers: Koszul complex over skew polynomial rings
For a commutative ring R with an ideal I, generated by a finite regular sequence, we construct differential graded algebras which provide R-free resolutions of I^s and of R/I^s for s>0 and which generalise the Koszul resolution. We derive…
We classify the squarefree ideals which are Gotzmann in a polynomial ring.
We propose a new definition of Koszulity for graded algebras where the degree zero part has finite global dimension, but is not necessarily semi-simple. The standard Koszul duality theorems hold in this setting. We give an application to…
This is a report on recent work of Chalupnik and Touze. We explain the Koszul duality for the category of strict polynomial functors and make explicit the underlying monoidal structure which seems to be of independent interest. Then we…
In this article we study the structure of residual intersections via constructing a finite complex which is acyclic under some sliding depth conditions on the cycles of the Koszul complex. This complex provides information on an ideal which…
This article concerns linear parts of minimal resolutions of finitely generated modules over commutative local, or graded rings. The focus is on the linearity defect of a module, which marks the point after which the linear part of its…
In this study, we investigate the binomial edge ring associated with the skew Ferrers diagram. By employing Sagbi basis theory, we construct a quadratic Gr\"{o}bner basis for its defining ideal. As an application, we prove that this ring is…
An explicit combinatorial minimal free resolution of an arbitrary monomial ideal $I$ in a polynomial ring in $n$ variables over a field of characteristic $0$ is defined canonically, without any choices, using higher-dimensional…
We show that diagonal subalgebras and generalized Veronese subrings of a bigraded Koszul algebra are Koszul. We give upper bounds for the regularity of sidediagonal and relative Veronese modules and apply the results to symmetric algebras…
We construct a model for cohomology of a space $X$ equipped with a torus $T$ action, whose homotopy orbit space $X_{T}$ is formal. This model represents Koszul complex of its equivariant cohomology. Studying homological properties of…
We provide a new combinatorial approach to study the minimal free resolutions of edge ideals, that is, quadratic square-free monomial ideals. With this method we can recover most of the known results on resolutions of edge ideals with…
I find new equations for Chow varieties, their secant varieties, and an additional variety that arises in the study of depth 5 circuits by flattenings and Koszul Young flattenings. This enables a new lower bound for symmetric border rank of…
We develop techniques for constructing model structures on chain complexes valued in accessible exact categories, and apply this to show that for a closed symmetric monoidal, locally presentable exact category $\mathpzc{E}$ with exact…
The following corollary has been added: for general tetragonal curve $C$ of genus $g\ge 9$ the homogeneous coordinate ring of $C$ defined by the line bundle $K(-T)$, where $K$ is the canonical class, $T$ is the tetragonal series, is Koszul.…
Some general criteria to produce explicit free algebras inside the division ring of fractions of skew polynomial rings are presented. These criteria are applied to some special cases of division rings with natural involutions, yielding, for…
We extend the Koszul calculus defined on quadratic algebras by Berger, Lambre and Solotar, to N-homogeneous algebras. When N>2, the Koszul cup and cap products are defined by specific expressions, and they are compatible with the Koszul…
In math.QA/0506507 I. Gelfand and the authors introduced and studied a new class of algebras associated to directed graphs. In this paper we show that these algebras are Koszul for a large class of layered (i.e. ranked) graphs.
We use the multiplicative structure of the Koszul resolution to give short and simple proofs of some known estimates for the total dimension of the cohomology of spaces which admit free torus actions and analogous results for filtered…
We describe the progress in the last 10 years related to Koszul modules and syzygies of algebraic varieties. Topics discussed include the general theory of Koszul modules and resonance varieties, applications to Chen ranks of K\"ahler and…
We construct a "Koszul duality" equivalence relating the (diagrammatic) Hecke category attached to a Coxeter system and a given realization to the Hecke category attached to the same Coxeter system and the dual realization. This extends a…