Related papers: Free hyperplane arrangements over arbitrary fields
This paper studies the algebraic structure of a new class of hyperplane arrangement $A$ obtained by deleting two hyperplanes from a free arrangement. We provide information on the minimal free resolutions of the logarithmic derivation…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
We show that the deletion theorem of a free arrangement is combinatorial, i.e., whether we can delete a hyperplane from a free arrangement keeping freeness depends only on the intersection lattice. In fact, we give an explicit sufficient…
Every subarrangement of Weyl arrangements of type $ B_{\ell} $ is represented by a signed graph. Edelman and Reiner characterized freeness of subarrangements between type $ A_{\ell-1} $ and type $ B_{\ell} $ in terms of graphs. Recently,…
Notions of freedom and independence for hypergraphs of models of a theory are defined. Properties of these notions and their applications to some natural classes of theories are studied.
In this paper we study Cynk-Szemberg octic hyperplane arrangements from the perspective of homological properties of their derivation modules. In particular, we define the notion of the type of hyperplane arrangements that will be used in…
We consider the triple $(\mathcal{A},\mathcal{A}',\mathcal{A}^H)$ of hyperplane arrangements and the division of their characteristic polynomials. We show that the freeness of $\mathcal{A}^H$ and the division of $\chi(\mathcal{A};t)$ by…
We extend the relation between random matrices and free probability theory from the level of expectations to the level of all correlation functions (which are classical cumulants of traces of products of the matrices). We introduce the…
In this article we prove in the main theorem that, there is a bijection between the isomorphism classes of a certain type of real hyperplane arrangements on the one hand, and the antipodal pairs of convex cones of an associated…
A new relation between a class of complex polynomials with a good behavior at infinity studied by A. N\'emethi and A. Zaharia and the cohomology groups of affine complex hyperplane arrangement complements with rank one local system…
In this article, we study the $k$-Lefschetz properties for non-Artinian algebras, proving that several known results in the Artinian case can be generalized in this setting. Moreover, we describe how to characterize the graded algebras…
In the theory of hyperplane arrangements, the most important and difficult problem is the combinatorial dependency of several properties. In this atricle, we prove that Terao's celebrated addition-deletion theorem for free arrangements is…
The exhaustive study of the rigid symmetries of arbitrary free field theories is motivated, along several lines, as a preliminary step in the completion of the higher-spin interaction problem in full generality. Some results for the…
The purpose of this paper is to give new examples of families of free singularities. We first show that a generic equidimensional subspace arrangement is free. Furthermore, we show that a product of two reduced Cohen-Macaulay subspaces is…
We define covariantly a deformation of a given algebra, then we will see how it can be related to a deformation quantization of a class of observables in Quantum Field Theory. Then we will investigate the operator order related to this…
In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…
We develop the geometry of folding paths in Outer space and, as an application, prove that the complex of free factors of a free group of finite rank is hyperbolic.
Over an arbitrary field $\mathbb{F}$, let $p$ and $q$ be monic polynomials with degree $2$ in $\mathbb{F}[t]$. The free Hamilton algebra of the pair $(p,q)$ is the free noncommutative algebra in two generators $a$ and $b$ subject only to…
We describe a structure of PRO on hypermatrices. This structure allows us to define multilinear representations of PROs and in particular of free Pros. As an example of applications, we investigate the relations of the representations of…
We study plane curves over finite fields whose tangent lines at smooth $\mathbb{F}_q$-points together cover all the points of $\mathbb{P}^2(\mathbb{F}_q)$.