Stable mappings and logarithmic relative symplectic forms (Q1297998)

Let \(D\) be the image of a stable, weighted homogeneous map \(f: \mathbb{C}^n \to\mathbb{C}^{n+1}\), with \(\dim_\mathbb{C} \text{Ker} (df_0)=1\), 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 \(\omega\in \Omega^2 (\log D)\) which restricts to a non-degenerate holomorphic 2-form on the Milnor fibres of \(D\); for small values of \(n\), calculations with the computer algebra system Macaulay show that this restriction is closed, and is thus a holomorphic symplectic form. We conjecture that this is always the case.