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  • 1 Department of Mathematics, The Ohio State University 231 W. 18th avenue, Colombus, Ohio, OH 43210 USA
  • 2 Eötvös Loránd Tudományegyetem, Természettudományi Kar, Analízis Tanszék Pázmány Péter sétány 1/b H-1117 Budapest, Hungary
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For a   non-constant polynomial map f: Cn?Cn-1 we consider the monodromy representation on the cohomology group of its generic fiber. The main result of the paper determines its dimension and provides a natural basis for it. This generalizes the corresponding results of [2] or [10], where the case n=2 is solved. As  applications,  we verify the Jacobian conjecture for (f,g) when the generic fiber of f is either rational or elliptic. These are generalizations of the corresponding results of [5], [7], [8], [11] and [12], where the case  n=2 is treated.

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