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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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