Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2025-01-05T14:02:32.888Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Peter Orlik
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706, U.S.A. e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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