Compact complex manifolds: an extension of Meersseman's and López de Medrano-Verjovsky's construction

Frédéric Bosio[1]

  • [1] Université de Poitiers, Département de Mathématiques, UMR 6086, Boulevard Pierre et Marie Curie, BP 30179, 86962 Futuroscope Chasseneuil Cedex (France)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 5, page 1259-1297
  • ISSN: 0373-0956

Abstract

top
In this paper, we construct new compact complex manifolds as spaces of orbits of linear actions on ℂ n , generalizing Meersseman’s results. We also give some properties of our manifolds.

How to cite

top

Bosio, Frédéric. "Variétés complexes compactes : une généralisation de la construction de Meersseman et López de Medrano-Verjovsky." Annales de l’institut Fourier 51.5 (2001): 1259-1297. <http://eudml.org/doc/115948>.

@article{Bosio2001,
abstract = {Nous construisons de nouvelles variétés complexes compactes comme espaces d’orbites d’actions linéaires de $\{\mathbb \{C\}\}^n$, généralisant en cela les constructions de Meersseman. Nous donnons également certaines propriétés de ces variétés.},
affiliation = {Université de Poitiers, Département de Mathématiques, UMR 6086, Boulevard Pierre et Marie Curie, BP 30179, 86962 Futuroscope Chasseneuil Cedex (France)},
author = {Bosio, Frédéric},
journal = {Annales de l’institut Fourier},
keywords = {compact complex manifolds; complex abelian Lie groups; combinatorics on finite sets},
language = {fre},
number = {5},
pages = {1259-1297},
publisher = {Association des Annales de l'Institut Fourier},
title = {Variétés complexes compactes : une généralisation de la construction de Meersseman et López de Medrano-Verjovsky},
url = {http://eudml.org/doc/115948},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Bosio, Frédéric
TI - Variétés complexes compactes : une généralisation de la construction de Meersseman et López de Medrano-Verjovsky
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 5
SP - 1259
EP - 1297
AB - Nous construisons de nouvelles variétés complexes compactes comme espaces d’orbites d’actions linéaires de ${\mathbb {C}}^n$, généralisant en cela les constructions de Meersseman. Nous donnons également certaines propriétés de ces variétés.
LA - fre
KW - compact complex manifolds; complex abelian Lie groups; combinatorics on finite sets
UR - http://eudml.org/doc/115948
ER -

References

top
  1. D.N. Akhiezer, Lie group actions in complex analysis, Aspects of Math. (1995) Zbl0845.22001
  2. E. Calabi, B. Eckmann, A class of complex manifolds which are not algebraic, Annals of Math. 58 (1953), 494-500 Zbl0051.40304MR57539
  3. C. Camacho, N. Kuiper, J. Palis, The topology of holomorphic flows with singularities, Publ. Math. I.H.E.S. 48 (1979), 5-38 Zbl0411.58018MR516913
  4. A. Haefliger, Deformations of transversely holomorphic flows on spheres and deformations of Hopf manifolds, Comp. Math. 55 (1985), 241-251 Zbl0582.32026MR795716
  5. H. Hopf, Zur Topologie der komplexen Manifaltigkeiten, (1948), Studies and Essays presented to R. Courant, New York Zbl0033.02501MR23054
  6. M. Inoue, On surfaces of class V I I 0 , Invent. Math. 24 (1974), 269-310 Zbl0283.32019MR342734
  7. S. López de Medrano, The topology of the intersection of quadrics in ℝ n , Lecture Notes in Math. 1370 (1989), 280-292 Zbl0681.57020MR1000384
  8. S. López de Medrano, A. Verjovsky, A new family of complex compact non symplectic manifolds, Bol. Soc. Math. Bra. 28 (1997), 253-269 Zbl0901.53021MR1479504
  9. J.-J. Loeb, M. Nicolau, Holomorphic flows and complex structures on products of odd dimensional spheres, Math. Annalen 306 (1996), 781-817 Zbl0860.32001MR1418353
  10. J.-J. Loeb, M. Nicolau, On the complex geometry of a class of non-kählerian manifolds, Israel J. Math. 110 (1999), 371-379 Zbl0956.53050MR1750427
  11. L. Meersseman, Un procédé géométrique de construction de variétés compactes, complexes, non algébriques en dimension quelconque, (1998) 
  12. L. Meersseman, A new geometric construction of compact complex manifolds in any dimension, Math. Annalen 317 (2000), 79-115 Zbl0958.32013MR1760670
  13. J. Winkelmann, Complex analytic geometry of complex parallelizable manifolds, Mémoires S.M.F., nouv. série 72-73 (1998) Zbl0918.32015MR1654465

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.