Global Sebastiani-Thom theorem for polynomial maps. (English) Zbl 0739.32034

Némethi, András

J. Math. Soc. Japan 43, No. 2, 213-218 (1991).

Let \(f: \mathbb{C}^ k\to\mathbb{C}\) be a polynomial. Then there exists a finite set \(\Lambda_ f\subset\mathbb{C}\) such that \(f\) is a smooth fiber bundle over \(\mathbb{C}\backslash\Lambda_ f\). Therefore monodromy is defined for \(f\) on large circles.
The author shows: Let \(g: \mathbb{C}^ m\to\mathbb{C}\), \(h: \mathbb{C}^ n\to\mathbb{C}\) be polynomials, \(f:=g+h\). Then: a) \(\Lambda_ f\subset\Lambda_ g+\Lambda_ h\). b) The generic fiber of \(f\) is homotopic equivalent with the join space of the generic fibers of \(g\) and \(h\). c) The algebraic monodromy of \(f\) is induced by the join of the geometric monodromics of \(g\) and \(h\).

Reviewer: H.-J.Reiffen (Osnabrück)

MSC:

32S40	Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
14B05	Singularities in algebraic geometry

Keywords:

polynomial maps; monodromy