JournalscmhVol. 81 , No. 4DOI 10.4171/cmh/79

Gauss-Manin connections for arrangements, IV. Nonresonant eigenvalues

  • Daniel C. Cohen

    Louisiana State University, Baton Rouge, USA
  • Peter Orlik

    University of Wisconsin, Madison, United States
Gauss-Manin connections for arrangements, IV. Nonresonant eigenvalues cover

Abstract

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 11-form associated to the Gauss-Manin connection.