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G. Denham, A. I. Suciu, S. Yuzvinsky. Combinatorial covers and vanishing of cohomology. Selecta Mathematica, 22 (2), pp. 561-594, 2016.

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


Posted by Alexandru Ion Suciu


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