no. 4
Arithmetic Fujita approximation
[Approximation de Fujita arithmétique]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 43 (2010) no. 4, pp. 555-578.

On démontre un analogue arithmétique du théorème d’approximation de Fujita en géométrie d’Arakelov - conjecturé par Moriwaki - par les mesures associées aux ℝ-filtrations.

We prove an arithmetic analogue of Fujita’s approximation theorem in Arakelov geometry, conjectured by Moriwaki, by using measures associated to ℝ-filtrations.

DOI : 10.24033/asens.2127
Classification : 14G40
Keywords: Fujita approximation, Arakelov geometry
Mot clés : approximation de Fujita, géométrie d'Arakelov 
@article{ASENS_2010_4_43_4_555_0,
     author = {Chen, Huayi},
     title = {Arithmetic {Fujita} approximation},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {555--578},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 43},
     number = {4},
     year = {2010},
     doi = {10.24033/asens.2127},
     mrnumber = {2722508},
     zbl = {1202.14024},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.2127/}
}
TY  - JOUR
AU  - Chen, Huayi
TI  - Arithmetic Fujita approximation
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2010
SP  - 555
EP  - 578
VL  - 43
IS  - 4
PB  - Société mathématique de France
UR  - http://www.numdam.org/articles/10.24033/asens.2127/
DO  - 10.24033/asens.2127
LA  - en
ID  - ASENS_2010_4_43_4_555_0
ER  - 
%0 Journal Article
%A Chen, Huayi
%T Arithmetic Fujita approximation
%J Annales scientifiques de l'École Normale Supérieure
%D 2010
%P 555-578
%V 43
%N 4
%I Société mathématique de France
%U http://www.numdam.org/articles/10.24033/asens.2127/
%R 10.24033/asens.2127
%G en
%F ASENS_2010_4_43_4_555_0
Chen, Huayi. Arithmetic Fujita approximation. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 43 (2010) no. 4, pp. 555-578. doi : 10.24033/asens.2127. http://www.numdam.org/articles/10.24033/asens.2127/

[1] S. Boucksom, C. Favre & M. Jonsson, Differentiability of volumes of divisors and a problem of Teissier, J. Algebraic Geom. 18 (2009), 279-308. | MR | Zbl

[2] N. Bourbaki, Éléments de mathématique 1965. | MR | Zbl

[3] H. Chen, Convergence des polygones de Harder-Narasimhan, to appear in Mémoires de la SMF. | Numdam | MR | Zbl

[4] J.-P. Demailly, L. Ein & R. Lazarsfeld, A subadditivity property of multiplier ideals, Michigan Math. J. 48 (2000), 137-156. | MR | Zbl

[5] L. Ein, R. Lazarsfeld, M. Mustaţǎ, M. Nakamaye & M. Popa, Asymptotic invariants of line bundles, Pure Appl. Math. Q. 1 (2005), 379-403. | MR | Zbl

[6] L. Ein, R. Lazarsfeld, M. Mustaţă, M. Nakamaye & M. Popa, Restricted volumes and base loci of linear series, Amer. J. Math. 131 (2009), 607-651. | MR | Zbl

[7] T. Fujita, Approximating Zariski decomposition of big line bundles, Kodai Math. J. 17 (1994), 1-3. | MR | Zbl

[8] É. Gaudron, Pentes des fibrés vectoriels adéliques sur un corps global, Rend. Semin. Mat. Univ. Padova 119 (2008), 21-95. | Numdam | MR | Zbl

[9] H. Gillet & C. Soulé, On the number of lattice points in convex symmetric bodies and their duals, Israel J. Math. 74 (1991), 347-357. | MR | Zbl

[10] R. Lazarsfeld, Positivity in algebraic geometry. II, Ergebnisse Math. Grenzg. 49, Springer, 2004. | MR | Zbl

[11] R. Lazarsfeld & M. Mustață, Convex bodies associated to linear series, Ann. Sci. Éc. Norm. Supér. 42 (2009), 783-835. | Numdam | MR | Zbl

[12] A. Moriwaki, Arithmetic height functions over finitely generated fields, Invent. Math. 140 (2000), 101-142. | MR | Zbl

[13] A. Moriwaki, Continuity of volumes on arithmetic varieties, J. Algebraic Geom. 18 (2009), 407-457. | MR | Zbl

[14] A. Moriwaki, Continuous extension of arithmetic volumes, Int. Math. Res. Not. 2009 (2009), 3598-3638. | MR | Zbl

[15] A. Okounkov, Brunn-Minkowski inequality for multiplicities, Invent. Math. 125 (1996), 405-411. | MR | Zbl

[16] R. Rumely, C. F. Lau & R. Varley, Existence of the sectional capacity, Mem. Amer. Math. Soc. 145, 2000. | MR | Zbl

[17] S. Takagi, Fujita's approximation theorem in positive characteristics, J. Math. Kyoto Univ. 47 (2007), 179-202. | MR | Zbl

[18] X. Yuan, Big line bundles over arithmetic varieties, Invent. Math. 173 (2008), 603-649. | MR | Zbl

[19] X. Yuan, On volumes of arithmetic line bundles, preprint arXiv:0811.0226. | MR | Zbl

[20] O. Zariski, The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface, Ann. of Math. 76 (1962), 560-615. | MR | Zbl

[21] S. Zhang, Positive line bundles on arithmetic varieties, J. Amer. Math. Soc. 8 (1995), 187-221. | MR | Zbl

Cité par Sources :