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Comment: 18 p., will appear in the Advanced Studies in Pure Mathematics 58 = Proc. Algebraic and Arithmetic Structures of Moduli Spaces, Hokkaido University 2007
Comment: 91 pages, 2 figures, comments are encouraged!; v2 slight change to the introduction
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.
Comment: 25 pages; completely rewritten, 1 figure added
Comment: The bidouble plane description has been corrected (Sections 4.2 and 4.3)
Comment: 5 pages
Comment: 5 pages
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