Stable mappings and logarithmic relative symplectic forms

Let D be the image of a stable, weighted homogeneous map , with , and which is not a trivial deformation of a lower-dimensional map. By proving a variant of the Buchsbaum-Eisenbud structure theorem for grade 3 Gorenstein quotients, we show the existence of a form which restrictst to a non-degenerate holomorphic 2-form on the Milnor fibres of D; experiments with the computer algebra programme Macaulay suggest this restriction is closed, and is thus a holomorphic symplectic form. Received January 23, 1997; in final form July 15, 1998