Equidistribution towards the Green current for holomorphic maps
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 41 (2008) no. 2, p. 307-336

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 .

Soient f un endomorphisme holomorphe non-inversible d’un espace projectif et f n son itéré d’ordre n. Nous prouvons que l’image réciproque par f n d’une hypersurface générique (au sens de Zariski), proprement normalisée, converge vers le courant de Green associé à f quand n tend vers l’infini. Nous donnons également un résultat analogue pour les images réciproques des (1,1)-courants positifs fermés et un résultat similaire pour les automorphismes polynomiaux réguliers de k .

DOI : https://doi.org/10.24033/asens.2069
Classification:  37F10,  32H50,  32U05
Keywords: Green current, exceptional set, plurisubharmonic function, Lelong number, regular automorphism
@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},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 41},
     number = {2},
     year = {2008},
     pages = {307-336},
     doi = {10.24033/asens.2069},
     zbl = {1160.32029},
     mrnumber = {2468484},
     language = {en},
     url = {http://www.numdam.org/item/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/item/ASENS_2008_4_41_2_307_0/

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