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Structure of a neighbourhood of a complex compact submanifold in a complex manifold. (English) Zbl 0573.32029

This paper contains a detailed proof of the following result: Let N be a compact complex submanifold of codimension one. Assume that there is another compact submanifold \(\tilde N\) with \(N\cap \tilde N=\emptyset\), such that a transverse disk to N intersects \(\tilde N\) generically in one point. Then there is a proper holomorphic mapping \(\pi\) : \(U\to D\) of a neighbourhood U of N onto the unit disk D with \(\pi^{-1}(0)=N\) and \(d\pi\) \(\neq 0\) everywhere.
Reviewer: K.Lamotke

MSC:

32J15 Compact complex surfaces
32H99 Holomorphic mappings and correspondences
32C25 Analytic subsets and submanifolds