Add to ORKG27 pages, v2: the relation with the (pole order) spectrum is added, and the title is changed, v3: Cor. 5.5 is addedUsing the graded duality of the cohomology of the Koszul complexes defined by the partial derivatives of homogeneous polynomials with one-dimensional singular loci, we get some formulas for their Poincare series generalizing a well-known result in the isolated singularity case. We also show some relations with the spectrum in the sense of Steenbrink by introducing the pole order spectrum and using the pole order spectral sequence as well as the Gauss-Manin systems and the Brieskorn modules in a generalized sense
Following Dwork's indications, in this work we give a further elaboration and a list of corrections ...
AbstractIn this paper we study the multigraded Hilbert and Poincaré–Betti series of A=S/a, where S i...
Abstract. As noticed by Jouanolou, Hurwitz proved in 1913 ([Hu]) that, in the generic case, the Kosz...
Koszul algebras, introduced by Priddy, are positively graded K-algebras R whose residue fieldK has a...
AbstractSeveral spectral sequence techniques are used in order to derive information about the struc...
dissertationIn Chapter 2, we compute a semi-free resolution of the Koszul complex over its endomorph...
Each connected graded, graded-commutative algebra $A$ of finite type over a field $\Bbbk$ of charact...
AbstractThroughout this paper k denotes an algebraically closed field of characteristic p > 0, G den...
International audienceThe formal integrability of systems of partial differential equations plays a ...
Let k be a field and R a standard graded k-algebra. We denote by HR the homology algebra of the Kosz...
We define generalized Koszul modules and rings and develop a generalized Koszul theory for $\mathbb{...
AbstractThis paper is devoted to the study of the spectral sequence theory of graded modules and its...
Let $S=K[x_1,\ldots,x_n]$ be a polynomial ring over a field $K$ and $I$ a homogeneous ideal in $S$ g...
We revisit Schmidt's theorem connecting the Schmidt rank of a tensor with the codimension of a certa...
For every homogeneous ideal I in a polynomial ring R and for every p\leq dim R we consider the Koszu...
Following Dwork's indications, in this work we give a further elaboration and a list of corrections ...
AbstractIn this paper we study the multigraded Hilbert and Poincaré–Betti series of A=S/a, where S i...
Abstract. As noticed by Jouanolou, Hurwitz proved in 1913 ([Hu]) that, in the generic case, the Kosz...
Koszul algebras, introduced by Priddy, are positively graded K-algebras R whose residue fieldK has a...
AbstractSeveral spectral sequence techniques are used in order to derive information about the struc...
dissertationIn Chapter 2, we compute a semi-free resolution of the Koszul complex over its endomorph...
Each connected graded, graded-commutative algebra $A$ of finite type over a field $\Bbbk$ of charact...
AbstractThroughout this paper k denotes an algebraically closed field of characteristic p > 0, G den...
International audienceThe formal integrability of systems of partial differential equations plays a ...
Let k be a field and R a standard graded k-algebra. We denote by HR the homology algebra of the Kosz...
We define generalized Koszul modules and rings and develop a generalized Koszul theory for $\mathbb{...
AbstractThis paper is devoted to the study of the spectral sequence theory of graded modules and its...
Let $S=K[x_1,\ldots,x_n]$ be a polynomial ring over a field $K$ and $I$ a homogeneous ideal in $S$ g...
We revisit Schmidt's theorem connecting the Schmidt rank of a tensor with the codimension of a certa...
For every homogeneous ideal I in a polynomial ring R and for every p\leq dim R we consider the Koszu...
Following Dwork's indications, in this work we give a further elaboration and a list of corrections ...
AbstractIn this paper we study the multigraded Hilbert and Poincaré–Betti series of A=S/a, where S i...
Abstract. As noticed by Jouanolou, Hurwitz proved in 1913 ([Hu]) that, in the generic case, the Kosz...