Obstructions to generic embeddings

Details Obstructions to generic embeddings Obstructions to generic embeddings

2007-11-02

arxiv.org/abs/0711.0229v1

Ann. Inst. Fourier, Grenoble 52 (2002), 1785-1792

Mathematics

Complex Variables

Scientific paper

In Grauert's paper [G] it is noted that finite dimensionality of cohomology groups sometimes implies vanishing of these cohomomogy groups. Later on Laufer formulated a zero or infinity law for the cohomology groups of domains in Stein manifolds. In this paper we generalize Laufer's Theorem in [L] and its version for small domains of CR manifolds, proved in [Br], by considering Whitney cohomology on locally closed subsets and cohomology with supports for currents. With this approach we obtain a global result for CR manifolds generically embedded in a Stein manifold. Namely a necessary condition for global embedding into an open subset of a Stein manifold is that the de-bar-M-cohomology groups must be either zero or infinite dimensional.

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