Pseudoconvex-concave duality and regularization of currents. (English) Zbl 0960.32011

Demailly, Jean-Pierre

Schneider, Michael (ed.) et al., Several complex variables. Cambridge: Cambridge University Press. Math. Sci. Res. Inst. Publ. 37, 233-271 (1999).

The paper investigates some basic properties of Finsler metrics on holomorphic vector bundles in the perspective of obtaining geometric versions of the Serre duality theorem. A duality framework under which pseudo-convexity and pseudo-concavity properties get exchanged is established. These duality properties are related to several geometric problems, e.g., the conjecture of Hartshorne and Schneider.
Finally, a new shorter and more geometric proof of a basic regularization theorem for closed \((1,1)\)-currents is shown.
For the entire collection see [Zbl 0933.00014].

Reviewer: Viorel Vâjâitu (Bucureşti)

MSC:

32F10	\(q\)-convexity, \(q\)-concavity
32C30	Integration on analytic sets and spaces, currents
32J25	Transcendental methods of algebraic geometry (complex-analytic aspects)

Keywords:

Hartshorne-Schneider conjecture; plurisubharmonic function; regularization of currents; Finsler metrics; pseudoconvexity; pseudoconcavity