Critical points and resonance of hyperplane arrangements

D. Cohen, G. Denham, M. Falk, A. Varchenko

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1038-1057
Number of pages20
JournalCanadian Journal of Mathematics
Issue number5
StatePublished - Oct 2011


  • Critical set
  • Hyperplane arrangement
  • Master function
  • Resonant weights

ASJC Scopus subject areas

  • General Mathematics


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