On démontre un analogue arithmétique du théorème d’approximation de Fujita en géométrie d’Arakelov - conjecturé par Moriwaki - par les mesures associées aux -filtrations.
We prove an arithmetic analogue of Fujita’s approximation theorem in Arakelov geometry, conjectured by Moriwaki, by using measures associated to -filtrations.
@article{ASENS_2010_4_43_4_555_0,
author = {Chen, Huayi},
title = {Arithmetic Fujita approximation},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
volume = {43},
year = {2010},
pages = {555-578},
doi = {10.24033/asens.2127},
mrnumber = {2722508},
zbl = {1202.14024},
language = {en},
url = {http://dml.mathdoc.fr/item/ASENS_2010_4_43_4_555_0}
}
Chen, Huayi. Arithmetic Fujita approximation. Annales scientifiques de l'École Normale Supérieure, Tome 43 (2010) pp. 555-578. doi : 10.24033/asens.2127. http://gdmltest.u-ga.fr/item/ASENS_2010_4_43_4_555_0/
[1] , & , Differentiability of volumes of divisors and a problem of Teissier, J. Algebraic Geom. 18 (2009), 279-308. | MR 2475816 | Zbl 1162.14003
[2] , Éléments de mathématique 1965. | MR 219684 | Zbl 0136.03404
[3] , Convergence des polygones de Harder-Narasimhan, to appear in Mémoires de la SMF. | Numdam | MR 2768967 | Zbl 1208.14001
[4] , & , A subadditivity property of multiplier ideals, Michigan Math. J. 48 (2000), 137-156. | MR 1786484 | Zbl 1077.14516
[5] , , , & , Asymptotic invariants of line bundles, Pure Appl. Math. Q. 1 (2005), 379-403. | MR 2194730 | Zbl 1139.14008
[6] , , , & , Restricted volumes and base loci of linear series, Amer. J. Math. 131 (2009), 607-651. | MR 2530849 | Zbl 1179.14006
[7] , Approximating Zariski decomposition of big line bundles, Kodai Math. J. 17 (1994), 1-3. | MR 1262949 | Zbl 0814.14006
[8] , Pentes des fibrés vectoriels adéliques sur un corps global, Rend. Semin. Mat. Univ. Padova 119 (2008), 21-95. | Numdam | MR 2431505 | Zbl 1206.14047
[9] & , On the number of lattice points in convex symmetric bodies and their duals, Israel J. Math. 74 (1991), 347-357. | MR 1135244 | Zbl 0752.52008
[10] , Positivity in algebraic geometry. II, Ergebnisse Math. Grenzg. 49, Springer, 2004. | MR 2095472 | Zbl 1093.14500
[11] & , Convex bodies associated to linear series, Ann. Sci. Éc. Norm. Supér. 42 (2009), 783-835. | Numdam | MR 2571958 | Zbl 1182.14004
[12] , Arithmetic height functions over finitely generated fields, Invent. Math. 140 (2000), 101-142. | MR 1779799 | Zbl 1007.11042
[13] , Continuity of volumes on arithmetic varieties, J. Algebraic Geom. 18 (2009), 407-457. | MR 2496453 | Zbl 1167.14014
[14] , Continuous extension of arithmetic volumes, Int. Math. Res. Not. 2009 (2009), 3598-3638. | MR 2539186 | Zbl 1192.14022
[15] , Brunn-Minkowski inequality for multiplicities, Invent. Math. 125 (1996), 405-411. | MR 1400312 | Zbl 0893.52004
[16] , & , Existence of the sectional capacity, Mem. Amer. Math. Soc. 145, 2000. | MR 1677934 | Zbl 0987.14018
[17] , Fujita's approximation theorem in positive characteristics, J. Math. Kyoto Univ. 47 (2007), 179-202. | MR 2359108 | Zbl 1136.14004
[18] , Big line bundles over arithmetic varieties, Invent. Math. 173 (2008), 603-649. | MR 2425137 | Zbl 1146.14016
[19] , On volumes of arithmetic line bundles, preprint arXiv:0811.0226. | MR 2575090 | Zbl 1197.14023
[20] , The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface, Ann. of Math. 76 (1962), 560-615. | MR 141668 | Zbl 0124.37001
[21] , Positive line bundles on arithmetic varieties, J. Amer. Math. Soc. 8 (1995), 187-221. | MR 1254133 | Zbl 0861.14018