Variétés complexes compactes : une généralisation de la construction de Meersseman et López de Medrano-Verjovsky
Bosio, Frédéric
Annales de l'Institut Fourier, Tome 51 (2001), p. 1259-1297 / Harvested from Numdam
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Nous construisons de nouvelles variétés complexes compactes comme espaces d’orbites d’actions linéaires de ℂ n , généralisant en cela les constructions de Meersseman. Nous donnons également certaines propriétés de ces variétés.

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.

Publié le : 2001-01-01
DOI : https://doi.org/10.5802/aif.1855
Classification:  32Q99,  32M05,  05A05
Mots clés: variétés complexes compactes, groupes de Lie abéliens complexes, combinatoire sur les ensembles finis 
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     author = {Bosio, Fr\'ed\'eric},
     title = {Vari\'et\'es complexes compactes : une g\'en\'eralisation de la construction de Meersseman et L\'opez de Medrano-Verjovsky},
     journal = {Annales de l'Institut Fourier},
     volume = {51},
     year = {2001},
     pages = {1259-1297},
     doi = {10.5802/aif.1855},
     mrnumber = {1860666},
     zbl = {0994.32018},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_2001__51_5_1259_0}
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Bosio, Frédéric. Variétés complexes compactes : une généralisation de la construction de Meersseman et López de Medrano-Verjovsky. Annales de l'Institut Fourier, Tome 51 (2001) pp. 1259-1297. doi : 10.5802/aif.1855. http://gdmltest.u-ga.fr/item/AIF_2001__51_5_1259_0/

[Akh] D.N. Akhiezer Lie group actions in complex analysis, Aspects of Math. (1995) | Zbl 0845.22001

[CE] E. Calabi; B. Eckmann A class of complex manifolds which are not algebraic, Annals of Math., Tome 58 (1953), pp. 494-500 | Article | MR 57539 | Zbl 0051.40304

[CKP] C. Camacho; N. Kuiper; J. Palis The topology of holomorphic flows with singularities, Publ. Math. I.H.E.S., Tome 48 (1979), pp. 5-38 | Numdam | MR 516913 | Zbl 0411.58018

[Hae] A. Haefliger Deformations of transversely holomorphic flows on spheres and deformations of Hopf manifolds, Comp. Math., Tome 55 (1985), pp. 241-251 | Numdam | MR 795716 | Zbl 0582.32026

[Ho] H. Hopf Zur Topologie der komplexen Manifaltigkeiten, Studies and Essays presented to R. Courant, New York (1948) | MR 23054 | Zbl 0033.02501

[Ino] M. Inoue On surfaces of class VII 0 , Invent. Math., Tome 24 (1974), pp. 269-310 | Article | MR 342734 | Zbl 0283.32019

[LDM] S. López De Medrano The topology of the intersection of quadrics in ℝ n , Lecture Notes in Math., Tome 1370 (1989), pp. 280-292 | Article | MR 1000384 | Zbl 0681.57020

[LDMV] S. López De Medrano; A. Verjovsky A new family of complex compact non symplectic manifolds, Bol. Soc. Math. Bra., Tome 28 (1997) no. 2, pp. 253-269 | Article | MR 1479504 | Zbl 0901.53021

[LN1] J.-J. Loeb; M. Nicolau Holomorphic flows and complex structures on products of odd dimensional spheres, Math. Annalen, Tome 306 (1996), pp. 781-817 | Article | MR 1418353 | Zbl 0860.32001

[LN2] J.-J. Loeb; M. Nicolau On the complex geometry of a class of non-kählerian manifolds, Israel J. Math., Tome 110 (1999), pp. 371-379 | Article | MR 1750427 | Zbl 0956.53050

[Me] L. Meersseman Un procédé géométrique de construction de variétés compactes, complexes, non algébriques en dimension quelconque (1998) (Thèse de doctorat, Université de Lille 1)

[Me′] L. Meersseman A new geometric construction of compact complex manifolds in any dimension, Math. Annalen, Tome 317 (2000), pp. 79-115 | Article | MR 1760670 | Zbl 0958.32013

[Wi] J. Winkelmann Complex analytic geometry of complex parallelizable manifolds, Mémoires S.M.F., nouv. série, Tome 72-73 (1998) | Numdam | MR 1654465 | Zbl 0918.32015