Holomorphic foliations of codimension one transverse to polydiscs

This paper is about the geometry of holomorphic foliations. We prove that if a codimension one holomorphic foliation with singularities defined in a neighborhood of the closed polydisc (Delta(n)) over bar in C-n, ngreater than or equal to2 is transverse to the boundary partial derivative(Delta(n)) over bar in the sense that is a natural generalization of [ 2], then the foliation is the pull-back of a linear logarithmic foliation of hyperbolic type. We also give a geometric characterization of hyperbolic linear logarithmic foliations.