Foliated neighborhoods of exceptional submanifolds

Details Foliated neighborhoods of exceptional submanifolds Foliated neighborhoods of exceptional submanifolds

2011-10-17

arxiv.org/abs/1110.3666v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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