Related papers: Transversal Intersection of Monomial Ideals
We consider the intersections of fractal k-cubes of order n and intersections of their respective opposite l-faces. The main result of the paper is the theorem on representation of such intersection as the attractor of a graph-directed…
In this paper we introduce the class of ordered homomorphism ideals and prove that these ideals admit minimal cellular resolutions constructed as homomorphism complexes. As a key ingredient of our work, we introduce the class of cointerval…
It is shown that any set of nonzero monomial prime ideals can be realized as the stable set of associated prime ideals of a monomial ideal. Moreover, an algorithm is given to compute the stable set of associated prime ideals of a monomial…
In this paper, we prove that a squarefree monomial ideal of height 2 whose quotient ring is Cohen-Macaulay is set-theoretic complete intersection.
We provide a graph formula which describes an arbitrary monomial in {\omega} classes (also referred to as stable {\psi} classes) in terms of a simple family of dual graphs (pinwheel graphs) with edges decorated by rational functions in…
The intersection matrix of a simplicial complex has entries equal to the rank of the intersection of its facets. In [1] the authors prove the intersection matrix is enough to determine a triangulation of a surface up to isomorphism. In this…
In this paper we extend one direction of Fr\"oberg's theorem on a combinatorial classification of quadratic monomial ideals with linear resolutions. We do this by generalizing the notion of a chordal graph to higher dimensions with the…
We define the uniform face ideal of a simplicial complex with respect to an ordered proper vertex colouring of the complex. This ideal is a monomial ideal which is generally not squarefree. We show that such a monomial ideal has a linear…
We investigate, using the notion of linear quotients, significative classes of connected graphs whose monomial edge ideals, not necessarily squarefree, have linear resolution, in order to compute standard algebraic invariants of the…
We prove that the integral closures of the powers of a squarefree monomial ideal I equal the symbolic powers if and only if I is the edge ideal of a Fulkersonian hypergraph.
The main purpose of this paper is to investigate prime, primary, and maximal ideals of semirings. The localization and primary decomposition of ideals in semirings are also studied.
We study blowups of affine n-space with center an arbitrary monomial ideal and call monomial ideals that render smooth blowups tame ideals. We give a combinatorial criterion to decide whether the blowup is smooth and apply this criterion to…
The aim of this paper is to present a simple way to generate proper monomial rational maps between generalized balls and via the relations between generalized balls and bounded symmetric domains of type I, we suggest new examples of proper…
We characterize the monomial ideals $I\subset K[x_1,\ldots,x_n]$ with the property that the polarization $I^p$ and $I^{\sigma^n}:=$ the ideal obtained from $I$ by the $n$-th iterated squarefree operator $\sigma$ are isomorphic via a…
We introduce the combinatorial Lyubeznik resolution of monomial ideals. We prove that this resolution is isomorphic to the usual Lyubezbnik resolution. As an application, we give a combinatorial method to determine if an ideal is a…
We determine sets of elements which, under certain conditions, generate an intersection of ideals up to radical.
In this paper, we give an explicit formula for the Futaki invariants of complete intersections. The result is new in the case where the variety is smooth or has orbifold singularities.
We construct in complete intersection's case, elementary currents which describe the local ideal, and give a decomposition in it for holomorphic function.
In this paper, we introduce the concept of complementary edge ideals of graphs and study their algebraic properties and invariants.
The goal of this paper is to prove the theorem in the title.