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]

Alessandrini, Lucia ; Bassanelli, Giovanni

Annales de l'Institut Fourier, Tome 51 (2001), p. 99-108 / Harvested from Numdam

Résumé

On démontre que si $X$ est une variété fortement pseudoconvexe telle que $H_2(X,{\mathbb {Z}})$ soit de type fini et son ensemble exceptionnel $S$ de dimension 1, alors $X$ est plongeable dans ${\mathbb {C}}^m\times {\mathbb {C}}{\mathbb {P}}_n$ 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.

Abstract

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 $H_2(X,{\mathbb {Z}})$, is embeddable in ${\mathbb {C}}^m\times {\mathbb {C}}{\mathbb {P}}_n$ if and only if $X$ is Kähler, and this case occurs only when $S$ does not contain any effective curve which is a boundary.

Détail

Publié le : 2001-01-01

Zbl 0966.32008 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.1817
Classification:  32F10,  53B35
Mots clés: variétés 1-convexes, variétés kählériennes

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