Publications (31)
Deletion-Restriction for Logarithmic Forms on Multiarrangements
Takuro Abe, Graham Denham
We consider the behaviour of logarithmic differential forms on arrangements and multiarrangements of hyperplanes under the operations of deletion and restriction, extending early w…
Abelian duality and propagation of resonance
Graham Denham, Alexander I. Suciu, Sergey Yuzvinsky
We explore the relationship between a certain "abelian duality" property of spaces and the propagation properties of their cohomology jump loci. To that end, we develop the analogy…
Higher resonance varieties of matroids
Graham Denham
We present some new results about the resonance varieties of matroids and hyperplane arrangements. Though these have been the objects of ongoing study, most work so far has focusse…
Modular decomposition of the Orlik-Terao algebra of a hyperplane arrangement
Graham Denham, Mehdi Garrousian, Stefan Tohaneanu
Let A be a collection of n linear hyperplanes in k^l, where k is an algebraically closed field. The Orlik-Terao algebra of A is the subalgebra R(A) of the rational functions genera…
Homology of subgroups of right-angled Artin groups
Graham Denham
We describe the (co)homology of a certain family of normal subgroups of right-angled Artin groups that contain the commutator subgroup, as modules over the quotient group. We do so…
Equivariant Euler characteristics of discriminants of reflection groups
Graham Denham, Nicole Lemire
Let G be a finite, complex reflection group and f its discriminant polynomial. The fibers of f admit commuting actions of G and a cyclic group. The virtual character…