Related papers: On the Orlik--Terao ideal and the relation space o…
We construct a combinatorial generalization of the Leray models for hyperplane arrangement complements. Given a matroid and some combinatorial blowup data, we give a presentation for a bigraded (commutative) differential-graded algebra. If…
To every realizable oriented matroid there corresponds an arrangement of real hyperplanes. The homeomorphism type of the complexified complement of such an arrangement is completely determined by the oriented matroid. In this paper we study…
We consider arrangements of tropical hyperplanes where the apices of the hyperplanes are taken to infinity in certain directions. Such an arrangement defines a decomposition of Euclidean space where a cell is determined by its `type' data,…
This paper begins by extending the notion of a combinatorial configuration of points and lines to a combinatorial configuration of points and planes that we refer to as configurations of order $2$. We then proceed to investigate a further…
We study the Z/2-equivariant K-theory of the complement of the complexification of a real hyperplane arrangement. We compute the rational K and KO rings, and give two different combinatorial descriptions of the subring of the integral KO…
Drawing parallels with hyperplane arrangements, we develop the theory of arrangements of submanifolds. Given a smooth, finite dimensional, real manifold $X$ we consider a finite collection $\mathcal{A}$ of locally flat, codimension-1…
We give a recursive algorithm for computing the Orlik-Terao algebra of the Coxeter arrangement of type A_{n-1} as a graded representation of S_n, and we give a conjectural description of this representation in terms of the cohomology of the…
An ordered semiring is a commutative semiring equipped with a compatible preorder. Ordered semirings generalise both distributive lattices and commutative rings, and provide a convenient framework to unify certain aspects of lattice theory…
Yuzvinsky and Rose-Terao have shown that the homological dimension of the gradient ideal of the defining polynomial of a generic hyperplane arrangement is maximum possible. In this work one provides yet another proof of this result, which…
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 expand upon the notion of equivariant log concavity, and make equivariant log concavity conjectures for Orlik--Solomon algebras of matroids, Cordovil algebras of oriented matroids, and Orlik--Terao algebras of hyperplane arrangements. In…
We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite…
We use stratified Morse theory to construct a complex to compute the cohomology of the complement of a hyperplane arrangement with coefficients in a complex rank one local system. The linearization of this complex is shown to be the…
Motivated by the Hilbert-space model for quantum mechanics, we define a pre-Hilbert space logic to be a pair $(S,\el)$, where $S$ is a pre-Hilbert space and $\el$ is an orthocomplemented poset of orthogonally closed linear subspaces of $S$,…
The complement of an arrangement A of a finite number of affine hyperplanes in complex n-space has the structure of a poset of spaces indexed by the intersection poset, L(A). The space corresponding to G in L(A) is homotopy equivalent to…
For a reduced hyperplane arrangement we prove the analytic Twisted Logarithmic Comparison Theorem, subject to mild combinatorial arithmetic conditions on the weights defining the twist. This gives a quasi-isomorphism between the twisted…
Several papers have been written studying unexpected hypersurfaces. We say a finite set of points Z admits unexpected hypersurfaces if a general union of fat linear subspaces imposes less that the expected number of conditions on the ideal…
In 1994, Orlik and Terao introduced a commutative Artinian analog S/I(A) of the Orlik-Solomon algebra of a hyperplane arrangement A to answer a question of Aomoto. A central topic of investigation in the study of Artinian algebras is the…
In the present note we study certain arrangements of codimension $2$ flats in projective spaces, we call them "Fermat arrangements". We describe algebraic properties of their defining ideals. In particular, we show that they provide…
Let $B$ be an arrangement of linear complex hyperplanes in $C^d$. Then a classical result by Orlik \& Solomon asserts that the cohomology algebra of the complement can be constructed from the combinatorial data that are given by the…