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

Tien-Cuong Dinh·Nessim Sibony
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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.

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Tien-Cuong Dinh, Nessim Sibony. 2008-09-19. Super-potentials of positive closed currents, intersection theory and dynamics. https://arxiv.org/abs/math/0703702

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