Let be a meromorphic self-mapping of a compact Kähler manifold. We study the rate of decreasing of volumes under the iteration of . We use these volume estimates to construct the Green current of in a quite general setting.
Soit un endomorphisme méromorphe d’une variété kählérienne compacte. Nous étudions le taux de décroissance des volumes sous l’itération de . Nous utilisons les estimées obtenues pour construire le courant de Green de l’application dans un cadre très général.
Keywords: meromorphic mapping, volume estimates, Green current
Mot clés : application méromorphe, estimées de volume, courant de Green
Guedj, Vincent 1
@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 = {https://aif.centre-mersenne.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 SP - 2369 EP - 2386 VL - 54 IS - 7 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/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://aif.centre-mersenne.org/articles/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. https://aif.centre-mersenne.org/articles/10.5802/aif.2083/
[B 02] On the volume of a line bundle, Internat. J. Math, Volume 13 (2002) no. 10, pp. 1043-1063 | DOI | MR | Zbl
[Ca 01] Dynamique des automorphismes des surfaces , Acta Math, Volume 187 (2001) no. 1, pp. 1-57 | DOI | MR | Zbl
[CG 04] Invariant currents and dynamical Lelong numbers, J. Geom. Anal, Volume 14 (2004) no. 2, pp. 199-213 | MR | Zbl
[D 90] 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] Dynamics of bimeromorphic maps of surfaces, Amer. J. Math, Volume 123 (2001) no. 6, pp. 1135-1169 | DOI | MR | Zbl
[DPS 01] Pseudo-effective line bundles on compact Kähler manifolds, Internat. J. Math, Volume 12 (2001) no. 6, pp. 689-741 | DOI | MR | Zbl
[DS 04] Regularization of currents and entropy (2004) (Preprint) | Numdam | MR | Zbl
[FG 01] Dynamique des applications rationnelles des espaces multiprojectifs. Indiana Univ, Math. J, Volume 50 (2001) no. 2, pp. 881-934 | MR | Zbl
[FJ 03] 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] Dynamics of polynomial mappings of , Amer. J. Math, Volume 124 (2002) no. 1, pp. 75-106 | DOI | MR | Zbl
[G 03a] Equidistribution towards the Green current, Bull. Soc. Math. France, Volume 131 (2003) no. 3, pp. 359-372 | Numdam | MR | Zbl
[G 03b] Ergodic properties of rational mappings with large topological degree (To appear in Annals of Math.) | MR | Zbl
[GZ 04] Intrinsic capacities on compact Kähler manifolds (e-print, arXiv:math.CV/0401302) | Zbl
[K 00] 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] Dynamique des applications rationnelles de , Dynamique et géométrie complexes (Panorama et Synthèses) (1999) | Zbl
[Sk 72] Sous-ensembles analytiques d'ordre fini ou infini dans , Bull. Soc. Math. France, Volume 100 (1972), pp. 353-408 | Numdam | MR | Zbl
Cited by Sources: