Global Sebastiani-Thom theorem for polynomial maps (Q1176082)

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 \(h\).