# Obstructions to generic embeddings

Judith Brinkschulte^{[1]}; C. Denson Hill^{[2]}; Mauro Nacinovich^{[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)

Annales de l’institut Fourier (2002)

- Volume: 52, Issue: 6, page 1785-1792
- ISSN: 0373-0956

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topBrinkschulte, Judith, Denson Hill, C., and Nacinovich, Mauro. "Obstructions to generic embeddings." Annales de l’institut Fourier 52.6 (2002): 1785-1792. <http://eudml.org/doc/116027>.

@article{Brinkschulte2002,

abstract = {Let $F$ be a relatively closed subset of a Stein manifold. We prove that the
$\bar\{\partial \}$-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
$\bar\{\partial \}_M$-cohomology groups.},

affiliation = {Chalmers University of Technology & Göteborg University, Department of Mathematics, Göteborg (Suède); SUNY at Stony Brook, Department of Mathematics, Stony Brook NY 11794 (USA); Università di Roma "Tor Vergaga", Dipartimento di Matematica, Via della Ricerca Scientifica, 00133 Roma (Italie)},

author = {Brinkschulte, Judith, Denson Hill, C., Nacinovich, Mauro},

journal = {Annales de l’institut Fourier},

keywords = {$\bar\{\partial \}$-operator; tangential $CR$ operator; embedding of $CR$ manifolds; d-bar operator; tangential CR operator; embedding of CR manifolds},

language = {eng},

number = {6},

pages = {1785-1792},

publisher = {Association des Annales de l'Institut Fourier},

title = {Obstructions to generic embeddings},

url = {http://eudml.org/doc/116027},

volume = {52},

year = {2002},

}

TY - JOUR

AU - Brinkschulte, Judith

AU - Denson Hill, C.

AU - Nacinovich, Mauro

TI - Obstructions to generic embeddings

JO - Annales de l’institut Fourier

PY - 2002

PB - Association des Annales de l'Institut Fourier

VL - 52

IS - 6

SP - 1785

EP - 1792

AB - Let $F$ be a relatively closed subset of a Stein manifold. We prove that the
$\bar{\partial }$-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
$\bar{\partial }_M$-cohomology groups.

LA - eng

KW - $\bar{\partial }$-operator; tangential $CR$ operator; embedding of $CR$ manifolds; d-bar operator; tangential CR operator; embedding of CR manifolds

UR - http://eudml.org/doc/116027

ER -

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