Gauss-Manin Connections for Arrangements

Daniel C. Cohen, Peter Orlik

Published 2001-05-09, updated 2002-03-18Version 3

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.