Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T03:31:45.677Z Has data issue: false hasContentIssue false
  • English
  • Français

DIFFERENTIAL FORMS ON FREE AND ALMOST FREE DIVISORS

Published online by Cambridge University Press:  03 November 2000

DAVID MOND
DAVID MOND
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, [email protected]
Get access

Abstract

We introduce a variant of the usual K\"{a}hler forms on singular free divisors, and show that it enjoys the same depth properties as K\"{a}hler 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 $\{D(f_\lambda)\}_{\lambda\in \Lambda}$ of discriminants of a versal deformation $\{f_\lambda\}_{\lambda\in\Lambda}$ of a singularity of a mapping. 1991 Mathematics Subject Classification: 14B07, 14D05, 32S40.

Keywords

free divisordifferential form
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 81 , Issue 3 , November 2000 , pp. 587 - 617
Copyright
2000 London Mathematical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)