Document Type
Article
Publication Date
10-1-2011
Abstract
If Φλ is a master function corresponding to a hyperplane arrangement A and a collection of weights λ, we investigate the relationship between the critical set of Φλ, the variety defined by the vanishing of the one-form ωλ = d log and Φλ, the resonance of λ. For arrangements satisfying certain conditions, we show that if λ is resonant in dimension p, then the critical set of Φλ has codimension at most p. These include all free arrangements and all rank 3 arrangements. © Canadian Mathematical Society 2011.
Publication Source (Journal or Book title)
Canadian Journal of Mathematics
First Page
1038
Last Page
1057
Recommended Citation
Cohen, D., Denham, G., Falk, M., & Varchenko, A. (2011). Critical points and resonance of hyperplane arrangements. Canadian Journal of Mathematics, 63 (5), 1038-1057. https://doi.org/10.4153/CJM-2011-028-8