On démontre que si est une variété fortement pseudoconvexe telle que soit de type fini et son ensemble exceptionnel de dimension 1, alors est plongeable dans si et seulement si est une variété kählérienne; en outre cette condition est vérifiée si et seulement si ne contient aucune courbe effective qui est homologue à zéro.
In this paper we show that a 1-convex (i.e., strongly pseudoconvex) manifold , with 1- dimensional exceptional set and finitely generated second homology group , is embeddable in if and only if is Kähler, and this case occurs only when does not contain any effective curve which is a boundary.
Keywords: 1-convex manifolds, Kähler manifolds
Mot 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}, pages = {99--108}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {51}, number = {1}, year = {2001}, doi = {10.5802/aif.1817}, zbl = {0966.32008}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1817/} }
TY - JOUR AU - Alessandrini, Lucia AU - Bassanelli, Giovanni TI - On the embedding of 1-convex manifolds with 1-dimensional exceptional set JO - Annales de l'Institut Fourier PY - 2001 SP - 99 EP - 108 VL - 51 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1817/ DO - 10.5802/aif.1817 LA - en ID - AIF_2001__51_1_99_0 ER -
%0 Journal Article %A Alessandrini, Lucia %A Bassanelli, Giovanni %T On the embedding of 1-convex manifolds with 1-dimensional exceptional set %J Annales de l'Institut Fourier %D 2001 %P 99-108 %V 51 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1817/ %R 10.5802/aif.1817 %G en %F 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/articles/10.5802/aif.1817/
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