Related papers: The pinched Veronese is Koszul

Each connected graded, graded-commutative algebra $A$ of finite type over a field $\Bbbk$ of characteristic zero defines a complex of finitely generated, graded modules over a symmetric algebra, whose homology graded modules are called the…

We prove that for any knot $K$, there exists a one-vertex triangulation of the $3$-sphere containing an edge forming $K$. The proof is constructive, and based on fully augmented links. We use our method to produce ``complicated'' simplicial…

We study the module of Koszul cycles $Z_t(I,M)$ of a homogeneous ideal $I$ in a polynomial ring $S$ with respect to a graded module $M$. Under mild assumptions on the base field we prove that the regularity of $Z_t(I,S)$ is a subadditive…

We consider partitions of a set with $r$ elements ordered by refinement. We consider the simplicial complex $\bar{K}(r)$ formed by chains of partitions which starts at the smallest element and ends at the largest element of the partition…

This is a survey paper on commutative Koszul algebras and Castelnuovo-Mumford regularity. We describe several techniques to establish the Koszulness of algebras. We discuss variants of the Koszul property such as strongly Koszul, absolutely…

A Koszul-Vinberg manifold is a manifold $M$ endowed with a pair $(\nabla,h)$ where $\nabla$ is a flat connection and $h$ is a symmetric bivector field satisfying a generalized Codazzi equation. The geometry of such manifolds could be seen…

We classify the finite connected simple graphs whose edge rings are strongly Koszul. From the classification, it follows that if the edge ring is strongly Koszul, then its toric ideal possesses a quadratic Gr\"obner basis.

The Koszul homology algebra of a commutative local (or graded) ring $R$ tends to reflect important information about the ring $R$ and its properties. In fact, certain classes of rings are characterized by the algebra structure on their…

Koszul algebras with quadratic Groebner bases, called strong Koszul algebras, are studied. We introduce affine algebraic varieties whose points are in one-to-one correspondence with certain strong Koszul algebras and we investigate the…

Let $M$ and $N$ be two monomials of the same degree, and let $I$ be the smallest Borel ideal containing $M$ and $N$. We show that the toric ring of $I$ is Koszul by constructing a quadratic Gr\"obner basis for the associated toric ideal.…

Strongly Koszul algebras were introduced by Herzog, Hibi and Restuccia in 2000. The goal of the present paper is to provide an in-depth study of such algebras and to investigate how strong Koszulness interacts with the existence of a…

Let $(R,\mathfrak m, \mathsf k)$ be a complete intersection local ring, $K$ be the Koszul complex on a minimal set of generators of $\mathfrak m$, and $A=H(K)$ be its homology algebra. We establish exact sequences involving direct sums of…

The Koszul homology of modules of the polynomial ring $R$ is a central object in commutative algebra.It is strongly related with the minimal free resolution of these modules, and thus with regularity, Hilbert functions, etc. Here we…

In this note, we calculate the Koszul homology of the codimension 3 Gorenstein ideals. We find filtrations for the Koszul homology in terms of modules with pure free resolutions and completely describe these resolutions. We also consider…

We conjecture that the stable Khovanov homology of torus knots can be described as the Koszul homology of an explicit non-regular sequence of quadratic polynomials. The corresponding Poincare series turns out to be related to the…

We compute generators and relations for the basic algebra of a non-semisimple singular block of the restricted enveloping algebra of $\mathfrak{sl}_3$ over an algebraically closed field of characteristic $p>3$. Working directly with the…

In this paper we prove that if G is a connected, simply-connected, semi-simple algebraic group over an algebraically closed field of sufficiently large characteristic, then all the blocks of the restricted enveloping algebra (Ug)_0 of the…

Let $\kk$ be a field, $R$ a standard graded quadratic $\kk$-algebra with $\dim_{\kk}R_2\le 3$, and let $\ov\kk$ denote an algebraic closure of $\kk$. We construct a graded surjective Golod homomorphism $\varphi \colon P\to…

Let K_s be a (-2,3,2s+1)-type Pretzel knot (s >= 3) and E(K_s)(p/q) be a closed manifold obtained by Dehn surgery along K_s with a slope p/q. We prove that if q>0, p/q >= 4s+7 and p is odd, then E(K_s)(p/q) cannot contain an R-covered…

We classify the orbits of solids in the projective space $\text{PG}(5,q)$, $q$ even, under the setwise stabiliser $K \cong \text{PGL}(3,q)$ of the Veronese surface. For each orbit, we provide an explicit representative $S$ and determine two…