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Differential Forms on Free and Almost Free Divisors
Author(s) -
Mond David
Publication year - 2000
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s002461150001265x
Subject(s) - mathematics , hypersurface , fibration , pure mathematics , cohomology , singularity , gravitational singularity , connection (principal bundle) , complete intersection , differential form , analogy , mathematical analysis , geometry , homotopy , linguistics , philosophy
We introduce a variant of the usual Kähler forms on singular free divisors, and show that it enjoys the same depth properties as Kähler forms on isolated hypersurface singularities. Using these forms it is possible to describe analytically the vanishing cohomology, and the Gauss–Manin connection, in families of free divisors, in precise analogy with the classical description for the Milnor fibration of an isolated complete intersection singularity, due to Brieskorn and Greuel. This applies in particular to the family{ D ( f λ ) } λ ∈ Λof discriminants of a versal deformation{ f λ } λ ∈ Λof a singularity of a mapping. 1991 Mathematics Subject Classification : 14B07, 14D05, 32S40.