On the embedding of 1-convex manifolds with 1-dimensional exceptional set

Alessandrini, Lucia; Bassanelli, Giovanni

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 $H_2(X,\mathbb{Z})$ soit de type fini et son ensemble exceptionnel $S$ de dimension 1, alors $X$ est plongeable dans ${ℂ}^m\times ℂ{\mathbb{P}}_n$ 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.

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

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