Stable mappings and logarithmic relative symplectic forms

Let D be the image of a stable, weighted homogeneous map f : C-n --> Cn+l, with dim(C)Ker (df(0)) = 1, and which is not a trivial deformation of a low er-dimensional map. By proving a variant of the Buchsbaum-Eisenbud structur e theorem for grade 3 Gorenstein quotients. we show the existence of a form omega is an element of Omega(2)(log D) which restrictst to a non-degenerat e holomorphic 2-form on the Milnor fibres of D; experiments with the comput er algebra programme Macaulay suggest this restriction is closed, and is th us a holomorphic symplectic form.