Cohomology of the complement of a free divisor |
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| Authors: | Francisco J. Castro-Jimé nez Luis Narvá ez-Macarro David Mond |
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| Affiliation: | Departamento de Álgebra, Computación, Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41012 Sevilla, Spain ; Departamento de Álgebra, Computación, Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41012 Sevilla, Spain ; Mathematics Institute, University of Warwick, Coventry CV4 7AL, England |
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| Abstract: | We prove that if  is a ``strongly quasihomogeneous" free divisor in the Stein manifold  , and  is its complement, then the de Rham cohomology of  can be computed as the cohomology of the complex of meromorphic differential forms on  with logarithmic poles along  , 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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