In this paper, we study the minimal free resolution of lex-ideals over a Koszul toric ring. In particular, we study in which toric ring R all lexideals are componentwise linear. We give a certain necessity and sufficiency condition for this property, and show that lex-ideals in a strongly Koszul toric ring are componentwise linear. In addition, it is shown that, in the toric ring arising from t...

In this paper we describe the defining equations of the Rees algebra and the special fiber ring of a truncation I of a complete intersection ideal in a polynomial ring over a field with homogeneous maximal ideal m. To describe explicitly the Rees algebra R(I) in terms of generators and relations we map another Rees ring R(M) onto it, where M is the direct sum of powers of m. We compute a Gröbne...

Let f = (f 1 ; : : : ; f m) be a holomorphic mapping in a neighborhood of the origin in C n. We nd suucient condition, in terms of residue currents, for a smooth function to belong to the ideal in C k generated by f. If f is a complete intersection the condition is essentially necessary. More generally we give suucient condition for an element of class C k in the Koszul complex induced by f to ...

A hypersurface D in C n is a linear free divisor if the module of logarithmic vector fields along D has a basis of global linear vector fields. It is then defined by a homogeneous polynomial of degree n and its complement is an open orbit of an algebraic subgroup G D of Gln(C) whose Lie algebra g D can be identified with that of linear logarithmic vector fields along D. We classify all linear f...

This work is devoted to an intrinsic cohomology theory of Koszul-Vinberg algebras and their modules. Our results may be regarded as improvements of the attempt by Albert Nijenhuis in [NA]. The relationships between the cohomology theory developed here and some classical problems are pointed out, e.g. extensions of algebras and modules, and deformation theory. The real Koszul-Vinberg cohomology ...

This paper is devoted to Koszul property of the homogeneous coordinate algebra of a smooth complex algebraic curve in the projective space (the notion of a Koszul algebra is some homological refinement of the notion of a quadratic algebra, for precise definition see next section). It grew out from the attempt to understand methods of M. Finkelberg and A. Vishik in their paper [10] proving this ...

We show that the integral cohomology rings of moduli spaces stable rational marked curves are Koszul. This answers an open question Manin. Using machinery Koszul developed by Berglund, we compute homotopy Lie algebras those spaces, and obtain some estimates for Betti numbers their free loop in case torsion coefficients. also prove conjecture generalisations our main result.

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

In [8] we studied Koszulity of a family tAssd of operads depending on a natural number n ∈ N and on the degree d ∈ Z of the generating operation. While we proved that, for n ≤ 7, the operad tAssd is Koszul if and only if d is even, and while it follows from [4] that tAssd is Koszul for d even and arbitrary n, the (non)Koszulity of tAssd for d odd and n ≥ 8 remains an open problem. In this note ...

We study the topological heterotic ring in (0,2) Landau-Ginzburg models without a (2,2) locus. The ring elements correspond to elements of the Koszul cohomology groups associated to a zero-dimensional ideal in a polynomial ring, and the computation of half-twisted genus zero correlators reduces to a map from the first nontrivial Koszul cohomology group to complex numbers. This map is a generali...