On the Seifert form at infinity associated with polynomial maps
If a polynomial map \(f:{\mathbb C}^n\to {\mathbb C}\) has a nice behaviour at infinity (e.g. it is a ``good polynomial''), then the Milnor fibration at infinity exists; in particular, one can define the Seifert form at infinity \(\Gamma(f)\) associated with \(f\). In this paper we prove a Sebastiani--Thom type formula. Namely, if \(f:{\mathbb C}^n\to {\mathbb C}\) and \(g:{\mathbb C}^m\to {\mathbb C}\) are ``good'' polynomials, and we define \(h=f\oplus g: {\mathbb C}^{n+m}\to {\mathbb C}\) by \(h(x,y)=f(x)+g(y)\), then \(\Gamma(h)=(-1)^{mn} \Gamma(f)\otimes \Gamma(g)\). This is the global analogue of the local result, proved independently by K. Sakamoto and P. Deligne for isolated hypersurface singularities.
scientific article; zbMATH DE number 1336908
scientific article