Decay of volumes under iteration of meromorphic mappings
Annales de l'Institut Fourier, Volume 54 (2004) no. 7, pp. 2369-2386.

Let f be a meromorphic self-mapping of a compact Kähler manifold. We study the rate of decreasing of volumes under the iteration of f. We use these volume estimates to construct the Green current of f in a quite general setting.

Soit f un endomorphisme méromorphe d’une variété kählérienne compacte. Nous étudions le taux de décroissance des volumes sous l’itération de f. Nous utilisons les estimées obtenues pour construire le courant de Green de l’application f dans un cadre très général.

DOI: 10.5802/aif.2083
Classification: 32H50,  58F23,  58F15
Keywords: meromorphic mapping, volume estimates, Green current
Guedj, Vincent 1

1 Université Paul Sabatier, Laboratoire Emile Picard, UMR 5580, 118 route de Narbonne, 31062 TOULOUSE Cedex 04 (France)
@article{AIF_2004__54_7_2369_0,
     author = {Guedj, Vincent},
     title = {Decay of volumes under iteration of meromorphic mappings},
     journal = {Annales de l'Institut Fourier},
     pages = {2369--2386},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {54},
     number = {7},
     year = {2004},
     doi = {10.5802/aif.2083},
     zbl = {1069.32007},
     mrnumber = {2139697},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2083/}
}
TY  - JOUR
AU  - Guedj, Vincent
TI  - Decay of volumes under iteration of meromorphic mappings
JO  - Annales de l'Institut Fourier
PY  - 2004
DA  - 2004///
SP  - 2369
EP  - 2386
VL  - 54
IS  - 7
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.2083/
UR  - https://zbmath.org/?q=an%3A1069.32007
UR  - https://www.ams.org/mathscinet-getitem?mr=2139697
UR  - https://doi.org/10.5802/aif.2083
DO  - 10.5802/aif.2083
LA  - en
ID  - AIF_2004__54_7_2369_0
ER  - 
%0 Journal Article
%A Guedj, Vincent
%T Decay of volumes under iteration of meromorphic mappings
%J Annales de l'Institut Fourier
%D 2004
%P 2369-2386
%V 54
%N 7
%I Association des Annales de l’institut Fourier
%U https://doi.org/10.5802/aif.2083
%R 10.5802/aif.2083
%G en
%F AIF_2004__54_7_2369_0
Guedj, Vincent. Decay of volumes under iteration of meromorphic mappings. Annales de l'Institut Fourier, Volume 54 (2004) no. 7, pp. 2369-2386. doi : 10.5802/aif.2083. http://www.numdam.org/articles/10.5802/aif.2083/

[B 02] S. Boucksom On the volume of a line bundle, Internat. J. Math, Volume 13 (2002) no. 10, pp. 1043-1063 | DOI | MR | Zbl

[Ca 01] S. Cantat Dynamique des automorphismes des surfaces K3, Acta Math, Volume 187 (2001) no. 1, pp. 1-57 | DOI | MR | Zbl

[CG 04] D. Coman; V. Guedj Invariant currents and dynamical Lelong numbers, J. Geom. Anal, Volume 14 (2004) no. 2, pp. 199-213 | MR | Zbl

[D 90] J.-P. Demailly Singular Hermitian metrics on positive line bundles, Complex algebraic varieties (Bayreuth, 1990) (Lecture Notes in Math), Volume 1507 (1990), pp. 87-104 | Zbl

[DF 01] J. Diller; C. Favre Dynamics of bimeromorphic maps of surfaces, Amer. J. Math, Volume 123 (2001) no. 6, pp. 1135-1169 | DOI | MR | Zbl

[DPS 01] J.-P. Demailly; T. Peternell; M. Schneider Pseudo-effective line bundles on compact Kähler manifolds, Internat. J. Math, Volume 12 (2001) no. 6, pp. 689-741 | DOI | MR | Zbl

[DS 04] T.C. Dinh; N. Sibony Regularization of currents and entropy (2004) (Preprint) | Numdam | MR | Zbl

[FG 01] C. Favre; V. Guedj Dynamique des applications rationnelles des espaces multiprojectifs. Indiana Univ, Math. J, Volume 50 (2001) no. 2, pp. 881-934 | MR | Zbl

[FJ 03] C. Favre; M. Jonsson Brolin's theorem for curves in two complex dimensions, Ann. Inst. Fourier, Volume 53 (2003) no. 5, pp. 1461-1501 | DOI | EuDML | Numdam | MR | Zbl

[G 02] V. Guedj Dynamics of polynomial mappings of 2 , Amer. J. Math, Volume 124 (2002) no. 1, pp. 75-106 | DOI | MR | Zbl

[G 03a] V. Guedj Equidistribution towards the Green current, Bull. Soc. Math. France, Volume 131 (2003) no. 3, pp. 359-372 | Numdam | MR | Zbl

[G 03b] V. Guedj Ergodic properties of rational mappings with large topological degree (To appear in Annals of Math.) | MR | Zbl

[GZ 04] V. Guedj; A. Zeriahi Intrinsic capacities on compact Kähler manifolds (e-print, arXiv:math.CV/0401302) | Zbl

[K 00] C. Kiselman Ensembles de sous-niveau et images inverses des fonctions plurisousharmoniques, Bull. Sci. Math, Volume 124 (2000) no. 1, pp. 75-92 | DOI | MR | Zbl

[S 99] N. Sibony Dynamique des applications rationnelles de k , Dynamique et géométrie complexes (Panorama et Synthèses) (1999) | Zbl

[Sk 72] H. Skoda Sous-ensembles analytiques d'ordre fini ou infini dans n , Bull. Soc. Math. France, Volume 100 (1972), pp. 353-408 | Numdam | MR | Zbl

Cited by Sources: