Transactions of the American Mathematical Society

Author(s): Francisco J. Castro-Jiménez; Luis Narváez-Macarro; David Mond
Journal: Trans. Amer. Math. Soc. 348 (1996), 3037-3049.
MSC (1991): Primary 32S20, 32S25, 14F40; Secondary 52B30, 58C27
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Abstract: We prove that if $D$

is a ``strongly quasihomogeneous" free divisor in the Stein manifold $X$

, and

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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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 32S20, 32S25, 14F40, 52B30, 58C27

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: 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.
Copyright of article: Copyright 1996, American Mathematical Society

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