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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)
##### Keywords:
good polynomials; Milnor fibrations at infinity
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