Abelian duality and propagation of resonance

• Graham Denham ^[1] ; Alexander I. Suciu ^[2] ; Sergey Yuzvinsky ^[3]
  1. [1] University of Western Ontario

     University of Western Ontario

     Canadá

     
  2. [2] Northeastern University
  3. [3] University of Oregon

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 4, 2017, págs. 2331-2367
• Idioma: inglés
• DOI: 10.1007/s00029-017-0343-5
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• Resumen

  • 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, rightangled Artin groups, and Bestvina–Brady groups. Our approach brings to the fore the relevance of the Cohen–Macaulay condition in this combinatorial context.