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

##### MSC:
 32S40 Monodromy; relations with differential equations and $$D$$-modules (complex-analytic aspects) 14B05 Singularities in algebraic geometry
##### Keywords:
polynomial maps; monodromy
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