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On the Seifert form at infinity associated with polynomial maps. (English) Zbl 0933.32042
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.

MSC:
32S55 Milnor fibration; relations with knot theory
14F45 Topological properties in algebraic geometry
14L24 Geometric invariant theory
57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
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