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Gauss-Manin Connections for Arrangements

Daniel C. Cohen·Peter Orlik
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Abstract

We construct a formal connection on the Aomoto complex of an arrangement of hyperplanes, and use it to study the Gauss-Manin connection for the moduli space of the arrangement in the cohomology of a complex rank one local system. We prove that the eigenvalues of the Gauss-Manin connection are integral linear combinations of the weights which define the local system.

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Daniel C. Cohen, Peter Orlik. 2002-03-18. Gauss-Manin Connections for Arrangements. https://arxiv.org/abs/math/0105063

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