On the embedding problem for 1-convex spaces

Tan, Vo Van

doi:10.1090/S0002-9947-1979-0546914-7

On the embedding problem for $1$-convex spaces
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Trans. Amer. Math. Soc. 256 (1979), 185-197 Request permission

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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On the classification of

convex spaces

On the positivity of line bundles on

convex spaces

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