84 citations · 266 across the 26 of their papers we have counts for
7 papers · 1 filter
On Ziegler's conjectures for logarithmic derivations of arrangements
Takuro Abe, Graham Denham
In his paper and thesis in 1989, Ziegler posed several conjectures regarding commutative algebra related to hyperplane arrangements. In this article, we revisit two of them. One is…
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…
Lagrangian combinatorics of matroids
Federico Ardila, Graham Denham, June Huh
The Lagrangian geometry of matroids was introduced in [ADH20] through the construction of the conormal fan of a matroid M. We used the conormal fan to give a Lagrangian-geometric i…
Lagrangian geometry of matroids
Federico Ardila, Graham Denham, June Huh
We introduce the conormal fan of a matroid M, which is a Lagrangian analog of the Bergman fan of M. We use the conormal fan to give a Lagrangian interpretation of the Chern-Schwart…
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…
Eigenvectors for a random walk on a hyperplane arrangement
Graham Denham
We find explicit eigenvectors for the transition matrix of a random walk due to Bidegare, Hanlon and Rockmore. This is accomplished by using Brown and Diaconis' analysis of its sta…