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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Gauss-Manin connections for arrangements, III Formal connections


Authors: Daniel C. Cohen and Peter Orlik
Journal: Trans. Amer. Math. Soc. 357 (2005), 3031-3050
MSC (2000): Primary 32S22, 14D05, 52C35, 55N25
Published electronically: July 16, 2004
MathSciNet review: 2135734
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Abstract: We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a complex rank one local system. We define formal Gauss-Manin connection matrices in the Aomoto complex and prove that, for all arrangements and all local systems, these formal connection matrices specialize to Gauss-Manin connection matrices.


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Additional Information

Daniel C. Cohen
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: cohen@math.lsu.edu

Peter Orlik
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: orlik@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03621-9
PII: S 0002-9947(04)03621-9
Keywords: Hyperplane arrangement, local system, Gauss-Manin connection
Received by editor(s): July 15, 2003
Published electronically: July 16, 2004
Additional Notes: The first author was partially supported by Louisiana Board of Regents grant LEQSF(1999-2002)-RD-A-01 and by National Security Agency grant MDA904-00-1-0038, and the second author was partially supported by National Security Agency grant MDA904-02-1-0019
Article copyright: © Copyright 2004 American Mathematical Society