On the embedding of 1-convex manifolds with 1-dimensional exceptional set  [ Sur le plongement d'une variété 1-convexe avec ensemble exceptionnel de dimension 1 ]
Annales de l'Institut Fourier, Tome 51 (2001) no. 1, p. 99-108
On démontre que si X est une variété fortement pseudoconvexe telle que H 2 (X,) soit de type fini et son ensemble exceptionnel S de dimension 1, alors X est plongeable dans m × n si et seulement si X est une variété kählérienne; en outre cette condition est vérifiée si et seulement si S ne contient aucune courbe effective qui est homologue à zéro.
In this paper we show that a 1-convex (i.e., strongly pseudoconvex) manifold X, with 1- dimensional exceptional set S and finitely generated second homology group H 2 (X,), is embeddable in m × n if and only if X is Kähler, and this case occurs only when S does not contain any effective curve which is a boundary.
DOI : https://doi.org/10.5802/aif.1817
Classification:  32F10,  53B35
Mots clés: variétés 1-convexes, variétés kählériennes
@article{AIF_2001__51_1_99_0,
     author = {Alessandrini, Lucia and Bassanelli, Giovanni},
     title = {On the embedding of 1-convex manifolds with 1-dimensional exceptional set},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {51},
     number = {1},
     year = {2001},
     pages = {99-108},
     doi = {10.5802/aif.1817},
     zbl = {0966.32008},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2001__51_1_99_0}
}
Alessandrini, Lucia; Bassanelli, Giovanni. On the embedding of 1-convex manifolds with 1-dimensional exceptional set. Annales de l'Institut Fourier, Tome 51 (2001) no. 1, pp. 99-108. doi : 10.5802/aif.1817. http://www.numdam.org/item/AIF_2001__51_1_99_0/

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