Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables

Vincent Maillot

Mémoires de la Société Mathématique de France (2000)

  • Volume: 80, page III1-VI129
  • ISSN: 0249-633X

How to cite

top

Maillot, Vincent. "Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables." Mémoires de la Société Mathématique de France 80 (2000): III1-VI129. <http://eudml.org/doc/94931>.

@article{Maillot2000,
author = {Maillot, Vincent},
journal = {Mémoires de la Société Mathématique de France},
keywords = {Arakelov geometry; toric variety; arithmetic variety; admissible line bundle; integrable line bundle; arithmetic Chern class; generalized Chow ring; intersection theory; current; canonical height; Bernstein-Koushnirenko theorem; Newton polytopes},
language = {fre},
pages = {III1-VI129},
publisher = {Société mathématique de France},
title = {Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables},
url = {http://eudml.org/doc/94931},
volume = {80},
year = {2000},
}

TY - JOUR
AU - Maillot, Vincent
TI - Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables
JO - Mémoires de la Société Mathématique de France
PY - 2000
PB - Société mathématique de France
VL - 80
SP - III1
EP - VI129
LA - fre
KW - Arakelov geometry; toric variety; arithmetic variety; admissible line bundle; integrable line bundle; arithmetic Chern class; generalized Chow ring; intersection theory; current; canonical height; Bernstein-Koushnirenko theorem; Newton polytopes
UR - http://eudml.org/doc/94931
ER -

References

top
  1. [BeT] BEDFORD E. et TAYLOR B.A. — A new capacity for plurisubharmonic functions, Acta math. 149, (1982), p. 1-41. Zbl0547.32012MR84d:32024
  2. [BaT] BATYREV V.V. et TSCHINKEL Y. — Rational Points of Bounded Height on Compactifications of Anisotropic Tori, Internat. Math. Res. Notices 12, (1995), p. 591-635. Zbl0890.14008MR97a:14021
  3. [BGS] BOST J.-B., GILLET H. et SOULÉ C. — Heights of projective varieties and positive Green forms, J. Amer. Math. Soc. 7, (1994), p. 903-1027. Zbl0973.14013MR95j:14025
  4. [Bo] BOYD D.W. — Speculations concerning the range of Mahler's measure, Canad. Math. Bull. 24, (1981), p. 453-469. Zbl0474.12005MR83h:12002
  5. [Br] BRYLINSKI J.-L. — Éventails et variétés toriques, Séminaire sur les singularités des surfaces, Centre de Math. de l'École Polytechnique, Palaiseau 1976-1977, Lectures Notes in Math. 777, Springer-Verlag (1980). Zbl0431.14013
  6. [Da] DANILOV V.I. — The geometry of toric varieties, Russian Math. Surveys 33, (1978), p. 97-154; Uspekhi Mat. Nauk. 33, (1978), p. 85-134. Zbl0425.14013MR80g:14001
  7. [De1] DEMAILLY J.-P. — Courants positifs et théorie de l'intersection, Gaz. Math. 53, (1992), p. 131-158. Zbl0771.32010MR93f:32012
  8. [De2] DEMAILLY J.-P. — Monge-Ampère operators, Lelong numbers and intersection theory, in Complex Analysis and Geometry, Univ. Ser. Math., (1993), p. 115-193. Zbl0792.32006MR94k:32009
  9. [De3] DEMAILLY J.-P. — Complex analytic and algebraic geometry, volume I, à paraître in Grundlehren für Math. Wissenschaften, Springer-Verlag. 
  10. [Dema] DEMAZURE M. — Sous-groupes algébriques de rang maximum du groupe de Cremona, Ann. Sci. École Norm. Sup. (4) 3, (1970), p. 507-588. Zbl0223.14009MR44 #1672
  11. [Den] DENINGER C. — Deligne periods of mixed motives, K-theory and the entropy of certain ℤn-actions, J. Amer. Math. Soc. 10, (1997), p. 259-281. Zbl0913.11027MR97k:11101
  12. [EGA2] GROTHENDIECK A. et DIEUDONNÉ J. — Éléments de géométrie algébrique II, Étude globale élémentaire de quelques classes de morphismes, Inst. Hautes Études Sci. Publ. Math. 8, (1961). Zbl0118.36206
  13. [EGA3] GROTHENDIECK A. et DIEUDONNÉ J. — Éléments de géométrie algébrique III, Étude cohomologique des faisceaux cohérents, Inst. Hautes Études Sci. Publ. Math. 11, (1961), et 17, (1963). Zbl0122.16102
  14. [Eh] EHLERS F. — Eine klasse komplexer Mannigfaltigkeiten und die Auflösung einiger isolierter Singularitäten, Math. Ann. 218, (1975), p. 127-156. Zbl0301.14003MR58 #11502
  15. [Fa] FALTINGS G. — Diophantine approximation on Abelian varieties, Ann. of Math. 133, (1991), p. 549-576. Zbl0734.14007MR93d:11066
  16. [FC] FALTINGS G. et CHAI C.-L. — Degeneration of abelian varieties, Springer-Verlag (1990). Zbl0744.14031MR92d:14036
  17. [FoS1] FORNÆSS J. E. et SIBONY N. — Complex dynamics in higher dimension II, in Modern methods in complex analysis (Princeton, NJ, 1992), Ann. of Math. Stud. 137, (1995), p. 135-182. Zbl0847.58059
  18. [FoS2] FORNÆS J. E. et SIBONY N. — Oka's inequality for currents and applications, Math. Ann. 301, (1995), p. 399-419. Zbl0832.32010MR96k:32013
  19. [Fu1] Fulton W. — Intersection Theory, Springer-Verlag (1984). Zbl0541.14005MR85k:14004
  20. [Fu2] FULTON W. — Introduction to toric varieties, Princeton University Press (1993). Zbl0813.14039MR94g:14028
  21. [FuS] FULTON W. et STURMFELS B. — Intersection theory on toric varieties, Topology 36, (1997), p. 335-353. Zbl0885.14025MR97h:14070
  22. [Gi] GILLET H. — Riemann-Roch theorems for higher algebraic K-theory, Adv. in Math. 40 no 3, (1981), p. 203-289. Zbl0478.14010MR83m:14013
  23. [GS1] GILLET H. et SOULÉ C. — Arithmetic intersection theory, Inst. Hautes Études Sci. Publ. Math. 72, (1990), p. 94-174. Zbl0741.14012MR92d:14016
  24. [GS2] GILLET H. et SOULÉ C. — Characteristic classes for algebraic vector bundles with Hermitian metrics I, II, Ann. of Math. 131 (1990), p. 163-203 et p. 205-238. Zbl0715.14018MR91m:14032a
  25. [GM] GORESKY M. et MACPHERSON R. — On the topology of algebraic torus actions, in Algebraic groups Utrecht 1986, Lecture Notes in Math. 1271, Springer-Verlag (1987), p. 73-90. Zbl0633.14025MR89a:14064
  26. [KKMS] KEMPF G., KNUDSEN F., MUMFORD D. ET SAINT-DONAT B. — Toroidal Embeddings I, Lecture Notes in Math. 339, Springer-Verlag (1973). Zbl0271.14017MR49 #299
  27. [Ko1] KOUSHNIRENKO A.G. — Polyhèdres de Newton et nombres de Milnor, Invent. math. 32, (1976), p. 1-31. Zbl0328.32007
  28. [Ko2] KOUSHNIRENKO A.G. — Newton polytopes and the Bézout theorem, Functional Analysis and its applications vol. 10, n° 3, (1976), p. 233-235. Zbl0341.32001
  29. [Lan] LANG S. — Algebraic Number Theory, Springer-Verlag (1970). Zbl0601.12001MR44 #181
  30. [Lau] LAURENT M. — Sur le théorème de Bézout, Prépublication LMD Luminy, 1994. 
  31. [Le1] LELONG P. — Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France 85, (1957), p. 239-262. Zbl0079.30901MR20 #2465
  32. [Le2] LELONG P. — Fonctions plurisousharmoniques de croissance logarithmique ; extension du résultant des polynômes, C. R. Acad. Sci. Paris Sér. I Math. 309, (1989), p. 315-320. Zbl0702.32016MR91c:32012
  33. [Le3] LELONG P. — Mesure de Mahler des polynômes et majoration par convexité, C. R. Acad. Sci. Paris Sér. I Math. 315, (1992), p. 139-142. Zbl0763.32003MR94a:32026
  34. [Ma1] MAILLOT V. — Un calcul de Schubert arithmétique, Duke Math. J. 80, (1995), p. 195-221. Zbl0867.14024MR97h:14039
  35. [Ma2] MAILLOT V. — Un théorème de Bernstein-Koushnirenko arithmétique, C. R. Acad. Sci. Paris Sér. I Math. 323, (1996), p. 977-980. Zbl0870.14015MR98c:14017
  36. [Ma3] MAILLOT V. — Géométrie d'Arakelov des grassmanniennes, des variétés toriques et de certaines hypersurfaces, Thèse, juin 1997. 
  37. [Oda] ODA T. — Convex Bodies and Algebraic Geometry, Springer-Verlag, (1988). Zbl0628.52002MR88m:14038
  38. [Ri] RICHBERG R. — Stetige streng pseudokonvexe Funktionen, Math. Ann. 175, (1968), p. 257-286. Zbl0153.15401MR36 #5386
  39. [Sm] SMYTH C.J. — On measures of polynomials in several variables, Bull. Austral. Math. Soc. 23, (1981), p. 49-63. Zbl0442.10034MR82k:10074
  40. [Zha] ZHANG S.S. — Small Points and Adelic Metrics, J. Algebraic Geom. 4, (1995), p. 281-300. Zbl0861.14019MR96e:14025

Citations in EuDML Documents

top
  1. Matthew H. Baker, Robert Rumely, Equidistribution of Small Points, Rational Dynamics, and Potential Theory
  2. Antoine Chambert-Loir, Amaury Thuillier, Mesures de Mahler et équidistribution logarithmique
  3. Carlos D’Andrea, Teresa Krick, Martín Sombra, Heights of varieties in multiprojective spaces and arithmetic Nullstellensätze
  4. Antoine Chambert-Loir, Points de petite hauteur sur les variétés semi-abéliennes
  5. Pascal Autissier, Équidistribution des sous-variétés de petite hauteur
  6. Éric Gaudron, Pentes des Fibrés Vectoriels Adéliques sur un Corps Global
  7. Jean-Benoît Bost, Gerard Freixas i Montplet, Semi-abelian Schemes and Heights of Cycles in Moduli Spaces of abelian Varieties

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.