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Commentarii Mathematici Helvetici

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Gauss-Manin connections for arrangements, IV. Nonresonant eigenvalues

Daniel C. Cohen (1) and Peter Orlik (2)

(1) Department of Mathematics, Louisiana State University, LA 70803, BATON ROUGE, UNITED STATES
(2) Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, WI 53706-1388, MADISON, UNITED STATES

An arrangement is a finite set of hyperplanes in a finite dimensional complex affine space. A complex rank one local system on the arrangement complement is determined by a set of complex weights for the hyperplanes. We study the Gauss-Manin connection for the moduli space of arrangements of fixed combinatorial type in the cohomology of the complement with coefficients in the local system determined by the weights. For nonresonant weights, we solve the eigenvalue problem for the endomorphisms arising in the $1$-form associated to the Gauss-Manin connection.

Keywords: Hyperplane arrangement, local system, Gauss-Manin connection