Polynomial functions and their behaviour at infinity

We consider polynomials as functions from $\mathbf C^n$ to $\mathrb C$. For certain values the topological type of the fibres can change (due to affine critical points or to “singularities at infinity”). Under certain conditions one can show that the generic fibre has the toplogy of a bouquet of spheres and that there exist invariants, which detect the values, where the function is not a fibration. Moreover we study deformations of polynomials, monodromy and relate this to boundary singualrities and Arnol'd's theory of fractions.
This is a joint research with M. Tibar.