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

Alessandrini, Lucia; Bassanelli, Giovanni

Alessandrini, Lucia; Bassanelli, Giovanni

Annales de l'Institut Fourier, Volume 51 (2001) no. 1, p. 99-108

Abstract
Résumé

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 $H_{2} (X, ℤ)$ , is embeddable in $ℂ^{m} \times ℂ ℙ_{n}$ if and only if $X$ is Kähler, and this case occurs only when $S$ does not contain any effective curve which is a boundary.

On démontre que si $X$ est une variété fortement pseudoconvexe telle que $H_{2} (X, ℤ)$ soit de type fini et son ensemble exceptionnel $S$ de dimension 1, alors $X$ est plongeable dans $ℂ^{m} \times ℂ ℙ_{n}$ 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.

Zbl 0966.32008 | 1 citation in Numdam

DOI : https://doi.org/10.5802/aif.1817
Classification: 32F10, 53B35
Keywords: 1-convex manifolds, Kähler manifolds

@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, Volume 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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