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

 

Cohomology of the complement of a free divisor


Authors: Francisco J. Castro-Jiménez, Luis Narváez-Macarro and David Mond
Journal: Trans. Amer. Math. Soc. 348 (1996), 3037-3049
MSC (1991): Primary 32S20, 32S25, 14F40; Secondary 52B30, 58C27
MathSciNet review: 1363009
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Abstract: We prove that if $D$ is a ``strongly quasihomogeneous" free divisor in the Stein manifold $X$, and $U$ is its complement, then the de Rham cohomology of $U$ can be computed as the cohomology of the complex of meromorphic differential forms on $X$ with logarithmic poles along $D$, with exterior derivative. The class of strongly quasihomogeneous free divisors, introduced here, includes free hyperplane arrangements and the discriminants of stable mappings in Mather's nice dimensions (and in particular the discriminants of Coxeter groups).


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Additional Information

Francisco J. Castro-Jiménez
Affiliation: Departamento de Álgebra, Computación, Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41012 Sevilla, Spain
Email: castro@atlas.us.es

Luis Narváez-Macarro
Affiliation: Departamento de Álgebra, Computación, Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41012 Sevilla, Spain
Email: narvaez@atlas.us.es

David Mond
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, England
Email: mond@maths.warwick.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01690-X
PII: S 0002-9947(96)01690-X
Received by editor(s): November 4, 1994
Additional Notes: The first two authors were supported by DGICYT PB94-1435.
Article copyright: © Copyright 1996 American Mathematical Society