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)
@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://archive.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://archive.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://archive.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://archive.numdam.org/articles/10.5802/aif.1817/

[1] L. Alessandrini; G. Bassanelli Metric properties of manifolds bimeromorphic to compact Kähler spaces, J. Differential Geom., Volume 37 (1993), pp. 95-121 | MR | Zbl

[2] C. Banica Sur les fibres infinitésimales d'un morphisme propre d'espaces complexes, Sém. F. Norguet, Fonctions de plusieurs variables complexes IV (Lect. Notes Math.), Volume 807 (1980) | Zbl

[3] G. Bassanelli A cut-off theorem for plurisubharmonic currents, Forum Math., Volume 6 (1994), pp. 567-595 | DOI | MR | Zbl

[4] M. Coltoiu On the embedding of 1-convex manifolds with 1-dimensional exceptional set, Comment. Math. Helv., Volume 60 (1985), pp. 458-465 | DOI | MR | Zbl

[5] M. Coltoiu On 1-convex manifolds with 1-dimensional exceptional set (Collection of papers in memory of Martin Jurchescu), Rev. Roum. Math. Pures Appl., Volume 43 (1998), pp. 97-104 | MR | Zbl

[6] M. Coltoiu On the Oka-Grauert principle for 1-convex manifolds, Math. Ann., Volume 310 (1998) no. 3, pp. 561-569 | DOI | MR | Zbl

[7] M. Coltoiu On Hulls of Meromorphy and a Class of Stein Manifolds, Ann. Scuola Norm. Sup., Volume XXVIII (1999), pp. 405-412 | Numdam | MR | Zbl

[8] S. Eto; H. Kazama; K. Watanabe On strongly q-pseudoconvex spaces with positive vector bundles, Mem. Fac. Sci. Kyushu Univ. Ser. A, Volume 28 (1974), pp. 135-146 | DOI | MR | Zbl

[9] R. Harvey; J.R. Lawson An intrinsec characterization of Kähler manifolds, Invent. Math., Volume 74 (1983), pp. 169-198 | DOI | MR | Zbl

[10] M.L. Michelson On the existence of special metrics in complex geometry, Acta Math., Volume 143 (1983), pp. 261-295 | MR | Zbl

[11] R. Narasimhan The Levi problem for complex spaces II, Math. Ann., Volume 146 (1962), pp. 195-216 | DOI | MR | Zbl

[12] H.H. Schäfer Topological Vector Spaces, Graduate Texts in Mathematics, 3, Springer, 1970 | Zbl

[13] M. Schneider Familien negativer Vektorbündel und 1-convexe Abbilungen, Abh. Math. Sem. Univ. Hamburg, Volume 47 (1978), pp. 150-170 | DOI | MR | Zbl

[14] A. Silva Embedding strongly (1,1)-convex-concave spaces in m × n , Several complex variables (Proc. Sympos. Pure Math.), Volume Vol. XXX, Part 2 (1977), pp. 41-44 | Zbl

[15] Vo Van Tan Embedding theorems and Kählerity for 1-convex spaces, Comment. Math. Helv., Volume 57 (1982), pp. 196-201 | DOI | MR | Zbl

[16] Vo Van Tan On the Kählerian geometry of 1-convex threefolds, Forum Math., Volume 7 (1995), pp. 131-146 | DOI | MR | Zbl

Cité par Sources :