We prove an arithmetic analogue of Fujita’s approximation theorem in Arakelov geometry, conjectured by Moriwaki, by using measures associated to -filtrations.
On démontre un analogue arithmétique du théorème d’approximation de Fujita en géométrie d’Arakelov - conjecturé par Moriwaki - par les mesures associées aux -filtrations.
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://archive.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://archive.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://archive.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, Serie 4, Volume 43 (2010) no. 4, pp. 555-578. doi : 10.24033/asens.2127. http://archive.numdam.org/articles/10.24033/asens.2127/
[1] Differentiability of volumes of divisors and a problem of Teissier, J. Algebraic Geom. 18 (2009), 279-308. | MR | Zbl
, & ,[2] Éléments de mathématique 1965. | MR | Zbl
,[3] Convergence des polygones de Harder-Narasimhan, to appear in Mémoires de la SMF. | Numdam | MR | Zbl
,[4] A subadditivity property of multiplier ideals, Michigan Math. J. 48 (2000), 137-156. | MR | Zbl
, & ,[5] Asymptotic invariants of line bundles, Pure Appl. Math. Q. 1 (2005), 379-403. | MR | Zbl
, , , & ,[6] Restricted volumes and base loci of linear series, Amer. J. Math. 131 (2009), 607-651. | MR | Zbl
, , , & ,[7] Approximating Zariski decomposition of big line bundles, Kodai Math. J. 17 (1994), 1-3. | MR | Zbl
,[8] Pentes des fibrés vectoriels adéliques sur un corps global, Rend. Semin. Mat. Univ. Padova 119 (2008), 21-95. | Numdam | MR | Zbl
,[9] On the number of lattice points in convex symmetric bodies and their duals, Israel J. Math. 74 (1991), 347-357. | MR | Zbl
& ,[10] Positivity in algebraic geometry. II, Ergebnisse Math. Grenzg. 49, Springer, 2004. | MR | Zbl
,[11] Convex bodies associated to linear series, Ann. Sci. Éc. Norm. Supér. 42 (2009), 783-835. | Numdam | MR | Zbl
& ,[12] Arithmetic height functions over finitely generated fields, Invent. Math. 140 (2000), 101-142. | MR | Zbl
,[13] Continuity of volumes on arithmetic varieties, J. Algebraic Geom. 18 (2009), 407-457. | MR | Zbl
,[14] Continuous extension of arithmetic volumes, Int. Math. Res. Not. 2009 (2009), 3598-3638. | MR | Zbl
,[15] Brunn-Minkowski inequality for multiplicities, Invent. Math. 125 (1996), 405-411. | MR | Zbl
,[16] Existence of the sectional capacity, Mem. Amer. Math. Soc. 145, 2000. | MR | Zbl
, & ,[17] Fujita's approximation theorem in positive characteristics, J. Math. Kyoto Univ. 47 (2007), 179-202. | MR | Zbl
,[18] Big line bundles over arithmetic varieties, Invent. Math. 173 (2008), 603-649. | MR | Zbl
,[19] On volumes of arithmetic line bundles, preprint arXiv:0811.0226. | MR | Zbl
,[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 | Zbl
,[21] Positive line bundles on arithmetic varieties, J. Amer. Math. Soc. 8 (1995), 187-221. | MR | Zbl
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