2021/12/26 by Avi Steiner, Steiner, Avi, Graham Denham +1
Mathematics · #Advanced Combinatorial Mathematics #Meromorphic and Entire Functions #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.2112.13462
We study the Hadamard product of the linear forms defining a hyperplane arrangement with those of its dual, which we view as generating an ideal in a certain polynomial ring. We use this ideal, which we call the ideal of pairs, to study logarithmic derivations and critical set varieties of arrangements in a way which is symmetric with respect to matroid duality. Our main result exhibits the variety of the ideal of pairs as a subspace arrangement whose components correspond to cyclic flats of the arrangement. As a corollary, we are able to give geometric explanations of some freeness and projective dimension results due to Ziegler and Kung--Schenck.