Foliated Neighborhoods Of Exceptional Submanifolds

The present article deals with the classification of neighborhoods of negatively embedded submanifolds A of a complex manifold X. The main tools we use are one-dimensional foliations whose set of singularities is A and which are normally attracting at A. The linearization of these foliations is provided under general cohomological conditions. As a consequence, an extension of the classical embedding theorem of Grauert is obtained.