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Gauss–Man i n Conne ction s for Arrangements, I E igenvalues

Published online by Cambridge University Press:  04 December 2007

Daniel C. Cohen  and
Peter Orlik
Daniel C. Cohen
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A. e-mail: cohen@math.lsu.edu
Peter Orlik
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706, U.S.A. e-mail: orlik@math.wisc.edu
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Abstract

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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.

Keywords

Gauss–Manin connectionhyperplane arrangementlocal system
Type
Research Article
Information
Compositio Mathematica , Volume 136 , Issue 3 , May 2003 , pp. 299 - 316
Copyright
© 2003 Kluwer Academic Publishers