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, pp. 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 : 10.5802/aif.1817
Classification : 32F10, 53B35
Keywords: 1-convex manifolds, Kähler manifolds
Mot clés : variétés 1-convexes, variétés kählériennes
Alessandrini, Lucia 1 ; Bassanelli, Giovanni 1

1 Università di Parma, Dipartimento di Matematica, Via Massimo d'Azeglio 85/A, 43100 Parma (Italie)
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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/articles/10.5802/aif.1817/

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