Related papers: Triples of arrangements and local systems

We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong…

Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…

In this paper, we study simplicial hyperplane arrangements in real projective $3$-space. We give a necessary condition for the characteristic polynomial to have only real roots, valid also for non-simplicial arrangements. As application, we…

Using a regularization with the properties of dimensional regularization, higher order local consistency conditions on one loop anomalies and divergent counterterms are given. They are derived without any a priori assumption on the form of…

The Euler characteristic of a very affine variety encodes the number of critical points of the likelihood equation on this variety. In this paper, we study the Euler characteristic of the complement of a hypersurface arrangement with…

A conjecture of Denef-Jacobs-Veys relates motivic principal value integrals of multivalued rational top-forms with cohomology support loci of rank one local systems. We give a stronger positive answer to this conjecture for hyperplane…

We survey the cohomology jumping loci and the Alexander-type invariants associated to a space, or to its fundamental group. Though most of the material is expository, we provide new examples and applications, which in turn raise several…

We construct a formal connection on the Aomoto complex of an arrangement of hyperplanes, and use it to study the Gauss-Manin connection for the moduli space of the arrangement in the cohomology of a complex rank one local system. We prove…

This paper is the first in a series. The main goal of the series is to present a geometric construction of certain remarkable tensor categories arising from quantum groups coresponding to the value of deformation parameter $q$ equal to a…

A hyperplane arrangement is called formal provided all linear dependencies among the defining forms of the hyperplanes are generated by ones corresponding to intersections of codimension two. The significance of this notion stems from the…

In this paper, we study equivariant cohomolgy theory of Hom Lie Triple Systems. Using this cohomology, we study 1-parameter formal deformation and central extensions of Hom Lie Triple Systems in the equivariant context.

We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality,…

Under what circumstances might every extension of a combinatorial structure contain more copies of another one than the original did? This property, which we call prolificity, holds universally in some cases (e.g., finite linear orders) and…

We find explicitly the multiplicities in the (mixed) trace cocharacter sequence of two $3\times 3$ matrices over a field of characteristic 0 and show that asymptotically they behave as polynomials of seventh degree. As a consequence we…

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…

The principle of similarity, or homophily, is often used to explain patterns observed in complex networks such as transitivity and the abundance of triangles (3-cycles). However, many phenomena from division of labor to protein-protein…

Let R^1(A,R) be the degree-one resonance variety over a field R of a hyperplane arrangement A. We give a geometric description of R^1(A,R) in terms of projective line complexes. The projective image of R^1(A,R) is a union of ruled…

We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the…

In this paper, we construct a seven-term exact sequence involving the cohomology groups of a group extension. Although the existence of such a sequence can be derived using spectral sequence arguments, there is little knowledge about some…

In this article there are two main results. The first result gives a formula, in terms of a log resolution, for the graded pieces of the Hodge filtration on the cohomology of a unitary local system of rank one on the complement of an…