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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the embedding problem for $ 1$-convex spaces


Author: Vo Van Tan
Journal: Trans. Amer. Math. Soc. 256 (1979), 185-197
MSC: Primary 32F10
DOI: https://doi.org/10.1090/S0002-9947-1979-0546914-7
MathSciNet review: 546914
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Abstract: In this paper we provide a necessary and sufficient condition for 1-convex spaces (i.e., strongly pseudoconvex spaces) which can be realized as closed analytic subvarieties in some $ {C^N} \times {P_M}$. A construction of some normal 3-dimensional 1-convex space which cannot be embedded in any $ {C^N} \times {P_M}$ is given. Furthermore, we construct explicitly a non-kählerian 3-dimensional 1-convex manifold which answers a question posed by Grauert.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1979-0546914-7
Keywords: 1-convex spaces, blowing down process, positive line bundles, precise vanishing theorem, Moishezon spaces, compact cycle homologous to zero, kähler manifolds
Article copyright: © Copyright 1979 American Mathematical Society