Some examples of \(1\)-convex non-embeddable threefolds. (English) Zbl 1174.32014

Bassanelli, Giovanni; Leoni, Marco

Rev. Roum. Math. Pures Appl. 52, No. 6, 611-617 (2007).

A constructive approach leads to a family of \(1\)-convex threefolds with exceptional curve \(C\) of type \((0, -2)\), which are not embeddable in \(\mathbb{C}^{m}\times\mathbb{CP}_{n}\). A real \(3\)-dimensional chain \(A\) whose boundary is the complex curve \(C\) is emphasized in order to prove that these threefolds are not Kähler. Particular cases are to be found in [M. Colţoiu, Rev. Roum. Math. Pures Appl. 43, No. 1-2, 97–104 (1998; Zbl 0932.32018)].

Reviewer: Gabriela Cristescu (Arad)

MSC:

32Q40	Embedding theorems for complex manifolds
32F10	\(q\)-convexity, \(q\)-concavity

Keywords:

embeddable variety; exceptional curve; threefold