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Gauss-Manin connections for arrangements, III Formal connections
Author(s):
Daniel
C.
Cohen;
Peter
Orlik
Journal:
Trans. Amer. Math. Soc.
357
(2005),
3031-3050.
MSC (2000):
Primary 32S22, 14D05, 52C35, 55N25
Posted:
July 16, 2004
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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:
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
Posted:
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
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Copyright
2004,
American Mathematical Society
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