Transforms of currents by modifications and 1-convex manifolds. (English) Zbl 1034.32009

Alessandrini, Lucia; Bassanelli, Giovanni

Osaka J. Math. 40, No. 3, 717-740 (2003).

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.

Reviewer: Viorel Vâjâitu (Bucureşti)

MSC:

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

Keywords:

1-convexity; \((1,1)\)-currents