Super-potentials of positive closed currents, intersection theory and dynamics

Details Super-potentials of positive closed currents, intersection theory and dynamics Super-potentials of positive closed currents, intersection theory and dynamics

2007-03-23

arxiv.org/abs/math/0703702v2

Mathematics

Complex Variables

80 pages, to appear in Acta Math

Scientific paper

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.

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