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

Abstract

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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 C R 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.

How to cite

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Brinkschulte, 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 -

References

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  9. C.D. Hill, M. Nacinovich, Duality and distribution cohomology of C R manifolds, Ann. Sc. Norm. Sup. Pisa 22 (1995), 315-339 Zbl0848.32003MR1354910
  10. H.B. Laufer, On the infinite dimensionality of the Dolbeault cohomology groups, Proc. Amer. Math. Soc 52 (1975), 293-296 Zbl0314.32008MR379887
  11. M. Nacinovich, On boundary Hilbert differential complexes, Ann. Polon. Math 46 (1985), 213-235 Zbl0606.58046MR841829
  12. M. Nacinovich, Poincaré lemma for tangential Cauchy-Riemann complexes, Math. Ann 268 (1984), 449-471 Zbl0574.32045MR753407
  13. M. Nacinovich, G. Valli, Tangential Cauchy-Riemann complexes on distributions, Ann. Mat. Pura Appl 146 (1987), 123-160 Zbl0631.58024MR916690
  14. S.-T. Yau, Kohn-Rossi cohomology and its application to the complex Plateau problem I, Ann. of Math 113 (1981), 67-110 Zbl0464.32012MR604043

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