no. 5
Complex analysis/Analytic geometry
A remark on the approximation of plurisubharmonic functions
[Une remarque sur l'approximation des fonctions pluri-sous-harmoniques]

Présenté par : Jean-Pierre Demailly

Kim, Dano1
1 Department of Mathematical Sciences, Seoul National University, Seoul, Republic of Korea
Comptes Rendus. Mathématique, Tome 352 (2014) no. 5, pp. 387-389.

Nous montrons par un exemple que le résultat de Demailly relatif à l'approximation d'une fonction pluri-sous-harmonique via les noyaux de Bergman ne produit pas en général une suite décroissante.

We show by an example that the Demailly approximation sequence of a plurisubharmonic function, constructed via Bergman kernels, is not a decreasing sequence in general.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.10.024
Kim, Dano 1

1 Department of Mathematical Sciences, Seoul National University, Seoul, Republic of Korea 
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Kim, Dano. A remark on the approximation of plurisubharmonic functions. Comptes Rendus. Mathématique, Tome 352 (2014) no. 5, pp. 387-389. doi : 10.1016/j.crma.2013.10.024. http://www.numdam.org/articles/10.1016/j.crma.2013.10.024/

[1] Błocki, Z. Some applications of the Ohsawa–Takegoshi extension theorem, Expo. Math., Volume 27 (2009) no. 2, pp. 125-135

[2] Demailly, J.-P. Regularization of closed positive currents and intersection theory, J. Algebr. Geom., Volume 1 (1992), pp. 361-409

[3] Demailly, J.-P. Analytic Methods in Algebraic Geometry, International Press, Boston, 2012

[4] Demailly, J.-P.; Peternell, T.; Schneider, M. Pseudo-effective line bundles on compact Khler manifolds, Int. J. Math., Volume 12 (2001) no. 6, pp. 689-741

[5] Lazarsfeld, R. (Ergeb. Math. Ihrer Grenzgeb.), Volume vol. 3, Springer-Verlag, Berlin (2004), pp. 48-49

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