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Non-embeddable 1-convex manifolds. (Variétés 1-convexes non plongeables.) (English. French summary) Zbl 1310.32033

Author’s abstract: We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable 1-convex manifold.{ }We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type \((1, -3)\). To this end we study small resolutions of \(cD_4\)-singularities.

MSC:

32S45 Modifications; resolution of singularities (complex-analytic aspects)
32F10 \(q\)-convexity, \(q\)-concavity
32T15 Strongly pseudoconvex domains
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