Holomorphic foliations of codimension one transverse to polydiscs

Abstract

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 ∆n in C, n ≥ 2 is transverse to the boundary ∂∆n 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.