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.
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G. Denham: Partially supported by NSERC (Canada).
A. I. Suciu: Partially supported by NSF Grant DMS-1010298 and NSA Grant H98230-13-1-0225.
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Denham, G., Suciu, A.I. & Yuzvinsky, S. Combinatorial covers and vanishing of cohomology. Sel. Math. New Ser. 22, 561–594 (2016). https://doi.org/10.1007/s00029-015-0196-8
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DOI: https://doi.org/10.1007/s00029-015-0196-8
Keywords
- Combinatorial cover
- Cohomology with local coefficients
- Spectral sequence
- Hyperplane arrangement
- Elliptic arrangement
- Toric complex
- Cohen–Macaulay property