Let is a Koszul algebra. More generally, we work in the setting of local rings and we show
that certain conditions on the multiplicative structure of Koszul homology imply strong …

Abstract Let R= S/I be a quotient of a standard graded polynomial ring S by an ideal I
generated by quadrics. If R is Koszul, a question of Avramov, Conca, and Iyengar asks …

The main goal of this paper is to size up the minimal graded free resolution of a
homogeneous ideal in terms of its generating degrees. By and large, this is too ambitious an …

Let R= 𝕂 [x 1,…, xn] and I⊂ R be a homogeneous ideal. We first obtain certain sufficient
conditions for the subadditivity condition of R/I. As a consequence, we prove that if I is …

The main goal of this paper is to size up the minimal graded free resolution of a
homogeneous ideal in terms of its generating degrees, by itself an ambitious objective. As …

This work concerns commutative algebras of the form R= Q∕ I, where Q is a standard
graded polynomial ring and I is a homogenous ideal in Q. It has been proposed that when R …

Let R be a standard graded commutative algebra over a field k, let K be its Koszul complex
viewed as a differential graded k-algebra, and let H be the homology algebra of K. This …

The deviations of a graded algebra are a sequence of integers that determine the Poincaré
series of its residue field and arise as the number of generators of certain DG algebras. In a …

We show that the Koszul homology algebra of a quotient of a polynomial ring by the edge
ideal of a forest is generated by the lowest linear strand. This provides a large class of …

The Koszul homology algebra of the second Veronese is generated by the lowest strand -
ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …