Related papers: Koszul complexes and pole order filtrations

The Euler-Koszul complex is the fundamental tool in the homological study of A-hypergeometric differential systems and functions. We compare Euler-Koszul homology with D-module direct images from the torus to the base space through orbits…

In this paper we prove a version of curved Koszul duality for Z/2Z-graded curved coalgebras and their coBar differential graded algebras. A curved version of the homological perturbation lemma is also obtained as a useful technical tool for…

We consider a filtration on the cohomology of the structure sheaf indexed by (not necessarily reduced) divisors ``at infinity''. We show that the filtered pieces have transfers morphisms, fpqc descent, and are so called cube invariant. In…

We prove that a general determinantal hypersurface of dimension 3 is nodal. Moreover, in terms of Chern classes associated with bundle morphisms, we derive a formula for the intersection homology Euler characteristic of a general…

In mixed characteristic and in equal characteristic $p$ we define a filtration on topological Hochschild homology and its variants. This filtration is an analogue of the filtration of algebraic $K$-theory by motivic cohomology. Its graded…

We introduce the notion of filtered perversity of a filtered differential complex on a complex analytic manifold $X$, without any assumptions of coherence, with the purpose of studying the connection between the pure Hodge modules and the…

We prove the factoriality of the following nodal threefolds: a complete intersection of hypersurfaces $F$ and $G\subset\mathbb{P}^{5}$ of degree $n$ and $k$ respectively, where $G$ is smooth, $|\mathrm{Sing}(F\cap…

Let $g$ be a reductive Lie algebra over a field of characteristic zero. Suppose $g$ acts on a complex of vector spaces $M$ by $i_\lambda$ and $L_\lambda$, which satisfy the identities as contraction and Lie derivative do for smooth…

We define a poset of partitions associated to an operad. We prove that the operad is Koszul if and only if the poset is Cohen-Macaulay. In one hand, this characterisation allows us to compute the homology of the poset. This homology is…

Let A and A! be dual Koszul algebras. By Positselski a filtered algebra U with gr U = A is Koszul dual to differential graded algebra (A!,d). We relate the module categories of this dual pair by a tensor-Hom adjunction. This descends to…

We compute the rational Betti cohomology groups of the coarse moduli spaces of geometrically marked Del Pezzo surfaces of degree three and four as representations of the Weyl groups of the corresponding root systems. The proof uses a blend…

The R\'emond resultant attached to a multiprojective variety and a sequence of multihomogeneous polynomials is a polynomial form in the coefficients of the polynomials, which vanishes if and only if the polynomials have a common zero on the…

Let $Z'\subset \mathbb{P}^{n}$ be a smooth projective hypersurface of degree $d>1$ and let $Z\to \mathbb{P}^n$ be the $\mu_d$-cover totally ramified along $Z'$. We relate full level $d$ structures on the primitive cohomology $Z'$ with full…

The aim of this paper is to introduce a new notion of sequences called dd-sequences and show that this notion may be convenient for studying the polynomial property of partial Euler-Poincare' characteristics of the Koszul complex with…

We define a basic class of algebras which we call homotopy path algebras. We find that such algebras always admit a cellular resolution and detail the intimate relationship between these algebras, stratifications of topological spaces, and…

We study the relation between a certain graded part of the Jacobian ring of a projective hypersurface and a certain graded quotient for the Hodge filtration of its primitive cohomology, in the case that the hypersurface has at most isolated…

In this paper the codimension of the complement to the set of factorial hypersurfaces of degree $d$ in ${\mathbb P}^N$ is estimated for $d\geqslant 4$, $N\geqslant 7$.

We study the Hodge filtration of the intersection cohomology Hodge module for toric varieties. More precisely, we study the cohomology sheaves of the graded de Rham complex of the intersection cohomology Hodge module and give a precise…

We prove the $\mathbb{Q}$-factoriality of a nodal hypersurface in $\mathbb{P}^{4}$ of degree $n$ with at most ${\frac{(n-1)^{2}}{4}}$ nodes and the $\mathbb{Q}$-factoriality of a double cover of $\mathbb{P}^{3}$ branched over a nodal…

We study a finite dimensional quadratic graded algebra R defined from a finite ranked poset. This algebra has been central to the study of the splitting algebra of the poset, A, as introduced by Gelfand, Retakh, Serconek and Wilson . The…