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Vietnam Journal of Mathematics 39:3 (2011) 369-379

Equidistribution of Varieties for Endomorphisms

of Projective Spaces

Tien-Cuong Dinh¹ and Nessim Sibony²

¹UPMC Univ Paris 06, UMR 7586, Institut de Math´ematiques de Jussieu,

F-75005 Paris, France

²Université Paris-Sud, Mathématique-Bâtiment 425, 91405 Orsay, France

Abstract. Let f be a non-invertible holomorphic endomorphism of the complex projective space P^k and fⁿ its iterate of order n. Let V be an algebraic subvariety of P^k which is generic in the Zariski sense. We give here a survey on the asymptotic equidistribution of the sequence f⁻ⁿ(V) when n goes to infinity.

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Published by Springer since January 2013