Vanishing results for the Aomoto complex of real hyperplane arrangements via minimality

Journal of Singularities
volume 14 (2016), 74-90

Received on 22 December 2015. Received in revised form on 24 June 2016.

DOI: 10.5427/jsing.2016.14e

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Abstract:

We prove vanishing results for the cohomology groups of the Aomoto complex over an arbitrary coefficient ring for real hyperplane arrangements. The proof uses the minimality of arrangements and descriptions of the Aomoto complex in terms of chambers. Our methods are used to present a new proof for the vanishing theorem of local system cohomology groups, a result first proved by Cohen, Dimca, and Orlik.

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