Variétés complexes compactes : une généralisation de la construction de Meersseman et López de Medrano-Verjovsky  [ Compact complex manifolds: an extension of Meersseman's and López de Medrano-Verjovsky's construction ]
Annales de l'Institut Fourier, Volume 51 (2001) no. 5, p. 1259-1297
In this paper, we construct new compact complex manifolds as spaces of orbits of linear actions on n , generalizing Meersseman’s results. We also give some properties of our manifolds.
Nous construisons de nouvelles variétés complexes compactes comme espaces d’orbites d’actions linéaires de n , généralisant en cela les constructions de Meersseman. Nous donnons également certaines propriétés de ces variétés.
DOI : https://doi.org/10.5802/aif.1855
Classification:  32Q99,  32M05,  05A05
Keywords: compact complex manifolds, complex abelian Lie groups, combinatorics on finite sets
@article{AIF_2001__51_5_1259_0,
     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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {51},
     number = {5},
     year = {2001},
     pages = {1259-1297},
     doi = {10.5802/aif.1855},
     mrnumber = {1860666},
     zbl = {0994.32018},
     language = {fr},
     url = {https://aif.centre-mersenne.org/item/AIF_2001__51_5_1259_0}
}
Variétés complexes compactes : une généralisation de la construction de Meersseman et López de Medrano-Verjovsky. Annales de l'Institut Fourier, Volume 51 (2001) no. 5, pp. 1259-1297. doi : 10.5802/aif.1855. https://aif.centre-mersenne.org/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 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