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Super-potentials of positive closed currents, intersection theory and dynamics. (English) Zbl 1227.32024

Authors’ abstract: We introduce a notion of super-potential for positive closed currents of bidegree \((p, p)\) on projective spaces. This gives a calculus on positive closed currents of arbitrary bidegree. We define in particular the intersection of such currents and the pull-back operator by meromorphic maps. One of the main tools is the introduction of structural discs in the space of positive closed currents which gives a “geometry” on that space. We apply the theory of super-potentials to construct Green currents for rational maps and to study equidistribution problems for holomorphic endomorphisms and for polynomial automorphisms.
Reviewer: Pei-Chu Hu (Jinan)

MSC:

32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables
32U40 Currents
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