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On the Kählerian geometry of 1-convex threefolds. (English) Zbl 0839.32003
The author is dealing with the biholomorphic embedding of 1-convex threefolds $$X$$ into $$\mathbb{C}^n \times \mathbb{P}_m$$ when the exceptional set $$S$$ of $$X$$ is infinitesimally projective (i.e. $$S^{(\nu)} = {\mathcal O}_x/I_S (\nu)$$ is projective algebraic for any $$\nu \geq 1$$, $$I_S$$ ideal sheaf defining $$S)$$. New criteria are proved which put in evidence the parallelism between the global structure of non-Kählerian 1-convex and non algebraic Moishezon 3-folds.
Reviewer: G.Tomassini (Pisa)

##### MSC:
 32Q15 Kähler manifolds 32F10 $$q$$-convexity, $$q$$-concavity 14J30 $$3$$-folds 32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)
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