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Transforms of currents by modifications and 1-convex manifolds. (English) Zbl 1034.32009
The following question is discussed. Let \(\pi:\widetilde X\to X\) be a proper modification of complex manifolds with center \(Z\) and exceptational divisor \(E\). In analogy with the definition of a strict transform of a hypersurface in \(X\), the authors consider the case of currents on \(X\). They give nice results for currents of bidegree \((1,1)\). As an application a result by the reviewer [ibid. 38, No. 2, 287–294 (2001; Zbl 0982.32010)] on the equivalence between embeddability and Kählerianity of certain 1-convex manifolds is generalized.

32F10 \(q\)-convexity, \(q\)-concavity
32E05 Holomorphically convex complex spaces, reduction theory