Equidistribution towards the Green current for holomorphic maps

Tien-Cuong Dinh; Nessim Sibony

Annales scientifiques de l'École Normale Supérieure (2008)

  • Volume: 41, Issue: 2, page 307-336
  • ISSN: 0012-9593

Abstract

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Let f be a non-invertible holomorphic endomorphism of a projective space and f n its iterate of order n . We prove that the pull-back by f n of a generic (in the Zariski sense) hypersurface, properly normalized, converges to the Green current associated to f when n tends to infinity. We also give an analogous result for the pull-back of positive closed ( 1 , 1 ) -currents and a similar result for regular polynomial automorphisms of  k .

How to cite

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Dinh, Tien-Cuong, and Sibony, Nessim. "Equidistribution towards the Green current for holomorphic maps." Annales scientifiques de l'École Normale Supérieure 41.2 (2008): 307-336. <http://eudml.org/doc/272150>.

@article{Dinh2008,
abstract = {Let $f$ be a non-invertible holomorphic endomorphism of a projective space and $f^n$ its iterate of order $n$. We prove that the pull-back by $f^n$ of a generic (in the Zariski sense) hypersurface, properly normalized, converges to the Green current associated to $f$ when $n$ tends to infinity. We also give an analogous result for the pull-back of positive closed $(1,1)$-currents and a similar result for regular polynomial automorphisms of $\mathbb \{C\}^k$.},
author = {Dinh, Tien-Cuong, Sibony, Nessim},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Green current; exceptional set; plurisubharmonic function; Lelong number; regular automorphism},
language = {eng},
number = {2},
pages = {307-336},
publisher = {Société mathématique de France},
title = {Equidistribution towards the Green current for holomorphic maps},
url = {http://eudml.org/doc/272150},
volume = {41},
year = {2008},
}

TY - JOUR
AU - Dinh, Tien-Cuong
AU - Sibony, Nessim
TI - Equidistribution towards the Green current for holomorphic maps
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2008
PB - Société mathématique de France
VL - 41
IS - 2
SP - 307
EP - 336
AB - Let $f$ be a non-invertible holomorphic endomorphism of a projective space and $f^n$ its iterate of order $n$. We prove that the pull-back by $f^n$ of a generic (in the Zariski sense) hypersurface, properly normalized, converges to the Green current associated to $f$ when $n$ tends to infinity. We also give an analogous result for the pull-back of positive closed $(1,1)$-currents and a similar result for regular polynomial automorphisms of $\mathbb {C}^k$.
LA - eng
KW - Green current; exceptional set; plurisubharmonic function; Lelong number; regular automorphism
UR - http://eudml.org/doc/272150
ER -

References

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