J. London Math. Soc. (2) 75 (2007) 99–115 C2007 London Mathematical Society doi:10.1112/jlms/jdl005 HOLOMORPHIC VECTOR FIELDS TRANSVERSE TO POLYDISCS

In this article, we study holomorphic vector fields transverse to the boundary of a polydisc in Cn, n 3. We prove that, under a suitable hypothesis of transversality with the boundary of the polydisc, the foliation is the pull-back of a linear hyperbolic foliation via a locally injective holomorphic map. This is the n 3 version for one-dimensional foliations of a previous result proved for n = 2 by Brunella and Sad and for codimension-one foliations by Ito and Scárdua. 1. Introduction an