Critical points and resonance of hyperplane arrangements

D. Cohen, G. Denham, Michael J Falk, A. Varchenko

Research output: Contribution to journalArticle

10 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1038-1057
Number of pages20
JournalCanadian Journal of Mathematics
Volume63
Issue number5
DOIs
StatePublished - Oct 2011

Fingerprint

Arrangement of Hyperplanes
Critical Set
Critical point
Arrangement
Hyperplane Arrangement
Codimension

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Critical points and resonance of hyperplane arrangements. / Cohen, D.; Denham, G.; Falk, Michael J; Varchenko, A.

In: Canadian Journal of Mathematics, Vol. 63, No. 5, 10.2011, p. 1038-1057.

Research output: Contribution to journalArticle

Cohen, D. ; Denham, G. ; Falk, Michael J ; Varchenko, A. / Critical points and resonance of hyperplane arrangements. In: Canadian Journal of Mathematics. 2011 ; Vol. 63, No. 5. pp. 1038-1057.
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