相关论文: A generalization of the Taylor complex constructio…

Let $Q=k[x_1,..., x_n]$ be a polynomial ring over a field $k$ with the standard $N^n$-grading. Let $\phi$ be a morphism of finite free $N^n$-graded $Q$-modules. We translate to this setting several notions and constructions that appear…

We develop a notion of linear strands for multigraded free resolutions, and we prove a multigraded generalization of Green's Linear Syzygy Theorem.

We give a necessary and sufficient condition on a homogeneous polynomial ideal for its Taylor complex to be exact. Then we give a combinatorial construction of a minimal resolution for ideals satisfying the above condition (in particular…

Let $\Bbbk$ be a field and let $I$ be a monomial ideal in the polynomial ring $Q=\Bbbk[x_1,\ldots,x_n]$. In her thesis, Taylor introduced a complex which provides a finite free resolution for $Q/I$ as a $Q$-module. Later, Gemeda constructed…

Let K be a field, let R=K[x_1,..., x_m] be a polynomial ring with the standard Z^m-grading (multigrading), let L be a Noetherian multigraded R-module, and let F: E --> G be a finite free multigraded presentation of L over R. Given a choice…

The Taylor resolution is a fundamental object in the study of free resolutions over the polynomial ring, due to its explicit formula, cellular/combinatorial structure, and applicability to any and all monomial ideals. This paper generalizes…

Given a monomial ideal in a polynomial ring over a field, we define the generalized Newton complementary dual of the given ideal. We show good properties of such duals including linear quotients and isomorphisms between the special fiber…

We express the multigraded Betti numbers of an arbitrary monomial ideal in terms of the multigraded Betti numbers of two basic classes of ideals. This decompo- sition has multiple applications. In some concrete cases, we use it to construct…

The free resolution and the Alexander dual of squarefree monomial ideals associated with certain subsets of distributive lattices are studied.

We use the lcm-lattice of a monomial ideal to study its minimal free resolutions. A new concept called a Taylor basis of a minimal free resolution is introduced and then used throughout the paper. We give a method of constructing minimal…

In this paper, we extend constructions and results for the Taylor complex to the generalized Taylor complex constructed by Herzog. We construct an explicit DG-algebra structure on the generalized Taylor complex and extend a result of…

A free resolution of free partially commutative monoids is constructed and with its help the homological dimension of these monoids is calculated.

Squarefree monomial ideals arising from finite meet-semilattices and their free resolutions are studied. For the squarefree monomial ideals corresponding to poset ideals in a distributive lattice the Alexander dual is computed.

Let $I$ be a square-free monomial ideal $I$ of projective dimension one. Starting with the Taylor complex on the generators of $I^r$, we use Discrete Morse theory to describe a CW complex that supports a minimal free resolution of $I^r$. To…

Given a square-free monomial ideal $I$, we define a simplicial complex labeled by the generators of $I^2$ which supports a free resolution of $I^2$. As a consequence, we obtain (sharp) upper bounds on the Betti numbers of the second power…

Let $R=\Bbbk[x_1,\..., x_n]$ and $M=R^s/I$ a multigraded squarefree module. We discuss the construction of cochain complexes associated to $M$ and we show how to interpret homological invariants of $M$ in terms of topological computations.…

We describe the Taylor and Lyubeznik resolutions as simplicial resolutions, and use them to show that the Scarf complex of a monomial ideal is the intersection of all its minimal free resolutions.

We construct a canonical free resolution for arbitrary monomial modules and lattice ideals. This includes monomial ideals and defining ideals of toric varieties, and it generalizes our joint results with Irena Peeva for generic ideals.

For any toric ideal $I$ in a polynomial ring $S$, we provide a combinatorial description of a free resolution of the integral closure of the $S$-module $S/I$. These new complexes arise from an extension of Bayer--Sturmfels' theory of…

This paper is concerned with the combinatorial description of the graded minimal free resolution of certain monomial algebras which includes toric rings. Concretely, we explicitly describe how the graded minimal free resolution of those…