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

Lucia Alessandrini[1]; Giovanni Bassanelli[1]

  • [1] Università di Parma, Dipartimento di Matematica, Via Massimo d'Azeglio 85/A, 43100 Parma (Italie)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 1, page 99-108
  • ISSN: 0373-0956

Abstract

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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 × 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.

How to cite

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Alessandrini, Lucia, and Bassanelli, Giovanni. "On the embedding of 1-convex manifolds with 1-dimensional exceptional set." Annales de l’institut Fourier 51.1 (2001): 99-108. <http://eudml.org/doc/115916>.

@article{Alessandrini2001,
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.},
affiliation = {Università di Parma, Dipartimento di Matematica, Via Massimo d'Azeglio 85/A, 43100 Parma (Italie); Università di Parma, Dipartimento di Matematica, Via Massimo d'Azeglio 85/A, 43100 Parma (Italie)},
author = {Alessandrini, Lucia, Bassanelli, Giovanni},
journal = {Annales de l’institut Fourier},
keywords = {1-convex manifolds; Kähler manifolds; strongly pseudoconvex complex space; 1-convex complex space; 1-convex complex manifold; strongly pseudoconvex complex manifold; Kähler manifold; exceptional set; embedding theorem},
language = {eng},
number = {1},
pages = {99-108},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the embedding of 1-convex manifolds with 1-dimensional exceptional set},
url = {http://eudml.org/doc/115916},
volume = {51},
year = {2001},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 1
SP - 99
EP - 108
AB - 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.
LA - eng
KW - 1-convex manifolds; Kähler manifolds; strongly pseudoconvex complex space; 1-convex complex space; 1-convex complex manifold; strongly pseudoconvex complex manifold; Kähler manifold; exceptional set; embedding theorem
UR - http://eudml.org/doc/115916
ER -

References

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