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

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].

### MSC:

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