Let be a non-invertible holomorphic endomorphism of a projective space and its iterate of order . We prove that the pull-back by of a generic (in the Zariski sense) hypersurface, properly normalized, converges to the Green current associated to when tends to infinity. We also give an analogous result for the pull-back of positive closed -currents and a similar result for regular polynomial automorphisms of .
Soient un endomorphisme holomorphe non-inversible d’un espace projectif et son itéré d’ordre . Nous prouvons que l’image réciproque par d’une hypersurface générique (au sens de Zariski), proprement normalisée, converge vers le courant de Green associé à quand tend vers l’infini. Nous donnons également un résultat analogue pour les images réciproques des -courants positifs fermés et un résultat similaire pour les automorphismes polynomiaux réguliers de .
Keywords: Green current, exceptional set, plurisubharmonic function, Lelong number, regular automorphism
Mot clés : courants de Green, ensemble exceptionnel, fonction plurisousharmonique, nombre de Lelong, automorphisme régulier
@article{ASENS_2008_4_41_2_307_0, author = {Dinh, Tien-Cuong and Sibony, Nessim}, title = {Equidistribution towards the {Green} current for holomorphic maps}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {307--336}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 41}, number = {2}, year = {2008}, doi = {10.24033/asens.2069}, mrnumber = {2468484}, zbl = {1160.32029}, language = {en}, url = {http://www.numdam.org/articles/10.24033/asens.2069/} }
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 SP - 307 EP - 336 VL - 41 IS - 2 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/asens.2069/ DO - 10.24033/asens.2069 LA - en ID - ASENS_2008_4_41_2_307_0 ER -
%0 Journal Article %A Dinh, Tien-Cuong %A Sibony, Nessim %T Equidistribution towards the Green current for holomorphic maps %J Annales scientifiques de l'École Normale Supérieure %D 2008 %P 307-336 %V 41 %N 2 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/asens.2069/ %R 10.24033/asens.2069 %G en %F ASENS_2008_4_41_2_307_0
Dinh, Tien-Cuong; Sibony, Nessim. Equidistribution towards the Green current for holomorphic maps. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 41 (2008) no. 2, pp. 307-336. doi : 10.24033/asens.2069. http://www.numdam.org/articles/10.24033/asens.2069/
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