-
Strongly pseudoconvex domains as subvarieties of complex manifolds
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 132, Number 2, April 2010
- pp. 331-360
- 10.1353/ajm.0.0106
- Article
- Additional Information
- Purchase/rental options available:
In this paper we obtain existence and approximation results for closed
complex subvarieties that are normalized by strongly pseudoconvex Stein
domains. Our sufficient condition for the existence of such subvarieties
in a complex manifold $X$ is expressed in terms of the Morse indices and
the number of positive Levi eigenvalues of an exhaustion function on $X$.
Examples show that our conditions cannot be weakened in general. We
obtain optimal results for subvarieties of this type in complements of
compact complex submanifolds with Griffiths positive normal bundle; in
the projective case these generalize classical theorems of Remmert,
Bishop and Narasimhan concerning proper holomorphic maps and embeddings
to ${\Bbb C}^n ={\Bbb P}^n \backslash {\Bbb P}^{n-1}$..