Foliated neighborhoods of exceptional submanifolds

Abstract

The present article is a study of germs of regular foliations transverse to an embedded strongly exceptional submanifold of a complex manifold. Cohomological conditions are given on this embedding for the existence of these foliations and their classification is established. One dimensional foliations singular at the submanifold and a generalization of a linearization theorem of Poincar\'e for these foliations, are used in this study. As a consequence of our approach, we obtain a refinement of the embedding theorem of Grauert.