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

Tien-Cuong Dinh Université Pierre et Marie Curie – Paris 6, Institut de Mathématiques de Jussieu Nessim Sibony Université Paris-Sud, Mathématique – Bâtiment 425

TBD mathscidoc:1701.332005

Acta Mathematica, 203, (1), 1-82, 2007.5
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.
super-potential; structural disc of currents; intersection theory; pull-back operator; complex dynamics; regular polynomial automorphism; algebraically; 37F
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  title={Super-potentials of positive closed currents, intersection theory and dynamics},
  author={Tien-Cuong Dinh, and Nessim Sibony},
  booktitle={Acta Mathematica},
Tien-Cuong Dinh, and Nessim Sibony. Super-potentials of positive closed currents, intersection theory and dynamics. 2007. Vol. 203. In Acta Mathematica. pp.1-82.
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