Selecta Mathematica

, Volume 23, Issue 4, pp 2331–2367 | Cite as

Abelian duality and propagation of resonance

  • Graham Denham
  • Alexander I. Suciu
  • Sergey Yuzvinsky


We explore the relationship between a certain “abelian duality” property of spaces and the propagation properties of their cohomology jump loci. To that end, we develop the analogy between abelian duality spaces and those spaces which possess what we call the “EPY property”. The same underlying homological algebra allows us to deduce the propagation of jump loci: in the former case, characteristic varieties propagate, and in the latter, the resonance varieties. We apply the general theory to arrangements of linear and elliptic hyperplanes, as well as toric complexes, right-angled Artin groups, and Bestvina–Brady groups. Our approach brings to the fore the relevance of the Cohen–Macaulay condition in this combinatorial context.


Duality space Abelian duality space Characteristic variety Resonance variety Propagation EPY property Hyperplane arrangement Toric complex Right-angled Artin group Bestvina–Brady group Cohen–Macaulay property 

Mathematics Subject Classification

Primary 55N25 Secondary 13C14 20F36 20J05 32S22 55U30 57M07 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Western OntarioLondonCanada
  2. 2.Department of MathematicsNortheastern UniversityBostonUSA
  3. 3.Department of MathematicsUniversity of OregonEugeneUSA

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