no. 6
Obstructions to generic embeddings
[Obstructions aux plongements génériques]
Brinkschulte, Judith1 ; Denson Hill, C.2 ; Nacinovich, Mauro3
1 Chalmers University of Technology \& Göteborg University, Department of Mathematics, Göteborg (Suède)
2 SUNY at Stony Brook, Department of Mathematics, Stony Brook NY 11794 (USA)
3 Università di Roma "Tor Vergaga", Dipartimento di Matematica, Via della Ricerca Scientifica, 00133 Roma (Italie)
Annales de l'Institut Fourier, Tome 52 (2002) no. 6, pp. 1785-1792.

Soit F un ensemble relativement fermé d’une variété de Stein. On prouve que les groupes de cohomologie associés à l’opérateur ∂ ¯ des formes de Whitney sur F et des courants à support dans F sont soit zéro, soit de dimension infinie. Cela nous permet d’obtenir une condition nécessaire pour l’existence d’un plongement CR générique d’une variété CR M dans un ouvert d’une variété de Stein : il faut que tous les groupes de cohomologie associés à l’opérateur ∂ ¯ M soient ou bien zéro ou bien de dimension infinie.

Let F be a relatively closed subset of a Stein manifold. We prove that the ∂ ¯-cohomology groups of Whitney forms on F and of currents supported on F are either zero or infinite dimensional. This yields obstructions of the existence of a generic CR embedding of a CR manifold M into any open subset of any Stein manifold, namely by the nonvanishing but finite dimensionality of some intermediate ∂ ¯ M -cohomology groups.

DOI : 10.5802/aif.1934
Classification : 32V05, 32V30
Keywords: $\bar{\partial }$-operator, tangential $CR$ operator, embedding of $CR$ manifolds
Mot clés : $\bar{\partial }$-opérateur, opérateur $CR$ tangentiel, plongement de variétés $CR$
Brinkschulte, Judith 1 ; Denson Hill, C. 2 ; Nacinovich, Mauro 3

1 Chalmers University of Technology \& Göteborg University, Department of Mathematics, Göteborg (Suède)
2 SUNY at Stony Brook, Department of Mathematics, Stony Brook NY 11794 (USA)
3 Università di Roma "Tor Vergaga", Dipartimento di Matematica, Via della Ricerca Scientifica, 00133 Roma (Italie) 
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Brinkschulte, Judith; Denson Hill, C.; Nacinovich, Mauro. Obstructions to generic embeddings. Annales de l'Institut Fourier, Tome 52 (2002) no. 6, pp. 1785-1792. doi : 10.5802/aif.1934. http://archive.numdam.org/articles/10.5802/aif.1934/

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