Building on work of Brandt and Terao in their study of k-formality, we introduce a co-chain
complex associated to a multi-arrangement and prove that its cohomologies determine …

This paper provides an overview of selected results and open problems in the theory of
hyperplane arrangements, with an emphasis on computations and examples. We give an …

We define a chain complex for generalized splines on graphs, analogous to that introduced
by Billera and refined by Schenck–Stillman for splines on polyhedral complexes. The …

Apolarity is a important tool in commutative algebra and algebraic geometry which studies a
form, f, by the action of polynomial differential operators on f. The quotient of all polynomial …

Free divisors form a celebrated class of hypersurfaces which has been extensively studied
in the past fifteen years. Our main goal is to introduce four new families of homogeneous …

Let A be an irreducible Coxeter arrangement and W be its Coxeter group. Then W naturally
acts on A. A multiplicity m: A→ Z is said to be equivariant when m is constant on each W …

In this note we study the freeness of the module of derivations on all moduli of the X 3
arrangement with multiplicities. We use homological techniques stemming from work of …

Only few categories of free arrangements are known in which Terao's conjecture holds. One
such category consists of 3-arrangements with unbalanced Ziegler restrictions. In this paper …

Building on work of Brandt and Terao in their study of $ k $-formality, we introduce a co-
chain complex associated to a multi-arrangement and prove that its cohomologies …

Definition 1.1 (Arrangement of hyperplanes). Let V be an l-dimensional vector space over a
field K. An affine subspace of dimension (l− 1) in V is called a hyperplane. An arrangement …