Selecta Mathematica

, Volume 22, Issue 2, pp 561–594

Combinatorial covers and vanishing of cohomology

  • Graham Denham
  • Alexander I. Suciu
  • Sergey Yuzvinsky
Article

DOI: 10.1007/s00029-015-0196-8

Cite this article as:
Denham, G., Suciu, A.I. & Yuzvinsky, S. Sel. Math. New Ser. (2016) 22: 561. doi:10.1007/s00029-015-0196-8
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Abstract

We use a Mayer–Vietoris-like spectral sequence to establish vanishing results for the cohomology of complements of linear and elliptic hyperplane arrangements, as part of a more general framework involving duality and abelian duality properties of spaces and groups. In the process, we consider cohomology of local systems with a general, Cohen–Macaulay-type condition. As a result, we recover known vanishing theorems for rank-1 local systems as well as group ring coefficients and obtain new generalizations.

Keywords

Combinatorial cover Cohomology with local coefficients Spectral sequence Hyperplane arrangement Elliptic arrangement Toric complex Cohen–Macaulay property 

Mathematics Subject Classification

Primary 55T99 Secondary 14F05 16E65 20J05 32S22 55N25 

Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Graham Denham
    • 1
  • Alexander I. Suciu
    • 2
  • Sergey Yuzvinsky
    • 3
  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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