Related papers: Triples of arrangements and local systems
A way to characterize the space of leaves of a foliation in terms of connections is proposed. A particular example of vertex algebra cohomology of codimension one foliations on complex curves is considered.
While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be…
We study Milnor fibers of complexified real line arrangements. We give a new algorithm computing monodromy eigenspaces of the first cohomology. The algorithm is based on the description of minimal CW-complexes homotopic to the complements,…
A {\it superpattern} is a string of characters of length $n$ that contains as a subsequence, and in a sense that depends on the context, all the smaller strings of length $k$ in a certain class. We prove structural and probabilistic results…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
We adapt and generalise results of Loganathan on the cohomology of inverse semigroups to the cohomology of ordered groupoids. We then derive a five-term exact sequence in cohomology from an extension of ordered groupoids, and show that this…
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.
In this article we introduce the space of configurations of commuting elements in a topological group and show that it satisfies rational homological stability for the sequences of unitary, special unitary and symplectic groups. We also…
We define the higher-order Alexander modules $A_{n,i}(\mathcal{U})$ and higher-order degrees $\delta_{n,i}(\mathcal{U})$ which are invariants of a complex hypersurface complement $\mathcal{U}$. These invariants come from the module…
Our work is concerned with simplicial complexes that describe higher-order interactions in real complex systems. This description allows to go beyond the pairwise node-to-node representation that simple networks provide and to capture a…
We construct an arithmetic analogue of the quantum local systems on the moduli of curves, and study its basic structure. Such an arithmetic local system gives rise to a uniform way of assigning a Galois cohomology class of the first…
We introduce a new topological invariant of complex line arrangements in the complex projective plane, derived from the interaction between their complement and the boundary of a regular neighbourhood. The motivation is to identify Zariski…
Lyubeznik conjectured that local cohomology modules of regular rings have finitely many associated primes. We examine this conjecture for polynomial rings over the integers, and record some equational identities that arise from studying…
We constructs a new network by superposition of hexahedron , which are scale-free, highly sparse,disassortative ,and maximal planar graphs. The network degree distribution, agglomeration coefficient and degree of correlation are computed…
We study the relative homology group of an affine hyperplane arrangement and its Poincar\'e dual, the cohomology at finite distance of the complement. We give an Orlik--Solomon-type description of the latter, and identify it with the vector…
We define several homology theories for central hyperplane arrangements, categorifying well-known polynomial invariants including the characteristic polynomial, Poincare polynomial, and Tutte polynomial. We consider basic algebraic…
The Euler characteristic of a very affine variety encodes the algebraic complexity of solving likelihood (or scattering) equations on this variety. We study this quantity for the Grassmannian with $d$ hyperplane sections removed. We provide…
We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…
We prove that the monodromy of an irreducible cohomologically complex rigid local system with finite determinant and quasi-unipotent local monodromies at infinity on a smooth quasiprojective complex variety $X$ is integral. This answers…
Combinatorial design theory studies set systems with certain balance and symmetry properties and has applications to computer science and elsewhere. This paper presents a modular approach to formalising designs for the first time using…