Diophantine approximations and foliations

Michael McQuillan

Publications Mathématiques de l'IHÉS (1998)

  • Volume: 87, page 121-174
  • ISSN: 0073-8301

How to cite


McQuillan, Michael. "Diophantine approximations and foliations." Publications Mathématiques de l'IHÉS 87 (1998): 121-174. <http://eudml.org/doc/104127>.

author = {McQuillan, Michael},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {second main theorem; Green-Griffiths conjecture; foliation},
language = {eng},
pages = {121-174},
publisher = {Institut des Hautes Études Scientifiques},
title = {Diophantine approximations and foliations},
url = {http://eudml.org/doc/104127},
volume = {87},
year = {1998},

AU - McQuillan, Michael
TI - Diophantine approximations and foliations
JO - Publications Mathématiques de l'IHÉS
PY - 1998
PB - Institut des Hautes Études Scientifiques
VL - 87
SP - 121
EP - 174
LA - eng
KW - second main theorem; Green-Griffiths conjecture; foliation
UR - http://eudml.org/doc/104127
ER -


  1. [A-S-S] E. ARRONDO, I. SOLS, B. SPEISER, Global Moduli For Contacts, MSRI preprint (1992). 
  2. [B-B] P. BAUM, R. BOTT, Singularities Of Holomorphic Foliations, J. Differential Geometry 7 (1972), 279-342. Zbl0268.57011MR51 #14092
  3. [B1] F. BOGOMOLOV, Families Of Curves On Surfaces Of General Type, Soviet Math. Dokl. 18 (1977), 1294-1297. Zbl0415.14013MR56 #15655
  4. [B2] F. BOGOMOLOV, Holomorphic tensors and vector bundles on projective varieties, Math. USSR Izv. 13 (1978), 499-555. Zbl0439.14002
  5. [Bo] E. BOMBIERI, The Mordell Conjecture Revisited, Ann. Scuola Norm. Sup. Pisa Cl. Sci (4) 17 (1990), n° 4, 615-640. Errata-corrigé : The Mordell conjecture revisited, Ann. Scuola Norm. Sup. Pisa Cl. Sci (4) 18 (1991), n° 3, 473. Zbl0722.14010
  6. [C] A. CONNES, Non Commutative Geometry, Academic Press, 1994. MR95j:46063
  7. [C-M] D. CERVEAU, J.-F. MATTEI, Formes intégrables holomorphes singulières, Astérisque vol. 97 (1982). Zbl0545.32006MR86f:58006
  8. [D] M. DESCHAMPS, Courbes de genres géométrique borné sur une surface de type général (d'après F. A. Bogomolov), Séminaire Bourbaki 519 (1977/1978). Zbl0412.14013
  9. [De1] J. P. DEMAILLY, Monge-Ampère operators, Lelong numbers, and intersection theory, Complex Analysis and Geometry, V. Ancona and A. Silva Eds, Plenum, New York, London (1993). Zbl0792.32006
  10. [De2] J. P. DEMAILLY, Algebraic Criteria for Kobayashi Hyperbolic Varieties and J et Differentials, Lecture notes of a course given at AMS summer research Institute, Santa Cruz (1995). 
  11. [De3] J. P. DEMAILLY, Regularization of closed positive currents and intersection theory, J AG 1 (1992), 361-409. Zbl0777.32016MR93e:32015
  12. [E] T. EKEDAHL, Foliations and Inseparable Morphisms, Algebraic Geometry, Bowdoin, Proc. Symp. Pure Math. 46, S. Bloch ed., AMS, Providence (1987), 139-149. Zbl0659.14018MR89d:14049
  13. [F] G. FALTINGS, Diophantine Approximation on abelian Varieties, Ann. Math. 133 (1991), 549-576. Zbl0734.14007MR93d:11066
  14. [Fu] W. FULTON, Intersection Theory, New York, Springer Verlag, Berlin, Heidelberg (1984). Zbl0541.14005MR85k:14004
  15. [Fuj] T. FUJITA, On the Zariski problem, Proc. Japan Acad. 55 (1979), 106-110. Zbl0444.14026MR80j:14029
  16. [G-G] M. GREEN, P. GRIFFITHS, Two applications of algebraic geometry to entire holomorphic mappings, The Chern Symposium, New York, Springer Verlag, Berlin, Heidelberg, (1979), 41-74. Zbl0508.32010MR82h:32026
  17. [H] R. HARTSHORNE, Ample subvarieties of algebraic varieties, LNM 156 (1970). Zbl0208.48901MR44 #211
  18. [J] J. P. JOUANOLOU, Hypersurface solutions d'une équation de Pfaff analytique, Math. Ann. 232 (1978), 239-245. Zbl0354.34007MR58 #1274
  19. [L1] S. LANG, Number Theory III, Encyclopedia of Mathematical Sciences, volume 60, New York, Springer Verlag, Berlin, Heidelberg, 1991. Zbl0744.14012MR93a:11048
  20. [L2] S. LANG, Introduction to complex hyperbolic spaces, New York, Springer Verlag, Berlin, Heidelberg (1987). Zbl0628.32001MR88f:32065
  21. [L-C] S. LANG, W. CHERRY, Topics In Nevanlinna Theory, LNM 1433 (1990). Zbl0709.30030MR91k:32025
  22. [L-Y] S. LU, S. T. YAU, Holomorphic curves in surfaces of general type, Proc. Nat. Acad. Sci. USA 87 (1990), 80-82. Zbl0702.32015MR91h:32021
  23. [M1] M. McQUILLAN, A new proof of the Bloch conjecture, JAG 5 (1996), 107-117. Zbl0862.14027MR96m:32028
  24. [M2] M. McQUILLAN, A Dynamical Counterpart To Faltings' Diophantine Approximation On Abelian Varieties, IHES preprint, 1996. 
  25. [M3] M. McQUILLAN, La mappa di Faltings e la construzione grafica di Macpherson, lectures given at the Università di Napoli, "Federico II", to appear. 
  26. [Mi1] Y. MIYAOKA, Algebraic Surfaces With Positive Index, Classification of algebraic and analytic manifolds (Kata Symposium Proc. 1982), Progress in Math. 39, Birkhauser, Boston Basel Stuttgart (1983), 281-301. Zbl0584.14022MR85j:14067
  27. [Mi2] Y. MIYAOKA, Deformations of Morphisms Along a Foliation, Algebraic Geometry, Bowdoin, Proc. Symp. Pure Math. 46, S. Bloch ed., AMS, Providence (1987), 245-268. Zbl0659.14008MR89e:14011
  28. [N] M. NAKAMAYE, conversation at tea, MSRI, 1992. 
  29. [No] J. NOGUCHI, On the value distribution of meromorphic mappings of covering spaces over Cm into algebraic varieties, J. Math. Soc. Japan 37 (1985), 295-313. Zbl0566.32019MR86g:32043
  30. [R] M. REID, Bogomolov's Theorem c21 ≤ 4c2, Proc. Intern. Colloq. Algebraic Geometry (Kyoto, 1977), 623-642. Zbl0478.14003MR82b:14014
  31. [S] A. SEIDENBERG, Reduction of singularities of the differential equation A dy = B dx, American Journ. Math. 89 (1967), 248-269. Zbl0159.33303
  32. [Sa] F. SAKAI, Weil Divisors on normal surfaces, Duke Math. J. 51 (1984), 877-887. Zbl0602.14006MR86m:14025
  33. [S-B] N. SHEPHERD-BARON, Miyaoka's Theorems, Flips And Abundance For Algebraic Threefolds (János Kollár ed.), Asterisque vol. 211 (1992), 103-114. Zbl0809.14034
  34. [Si] Y. T. SIU, Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math. (1974), 53-156. Zbl0289.32003MR50 #5003
  35. [So] C. SOULÉ, Lectures On Arakelov Geometry, Cambridge Studies in Advanced Mathematics 33, Cambridge, 1992. Zbl0812.14015MR94e:14031
  36. [U] E. ULLMO, Positivité et discrétion des points algébriques des courbes, to appear. Zbl0934.14013
  37. [V1] P. VOJTA, Diophantine Approximations and Value Distribution Theory, LNM 1239 (1987). Zbl0609.14011MR91k:11049
  38. [V2] P. VOJTA, On Algebraic Points On Curves, Comp. Math. 78 (1991), 29-36. Zbl0731.14015MR93b:11080
  39. [V3] P. VOJTA, Siegel's Theorem In The Compact Case, Ann. Math. 133 (1991), 509-548. Zbl0774.14019MR93d:11065
  40. [V4] P. VOJTA, Integral points on subvarieties of semi-abelian varieties I, to appear. Zbl1011.11040

Citations in EuDML Documents

  1. Julien Duval, Singularités des courants d'Ahlfors
  2. Erwan Rousseau, Degeneracy of holomorphic maps via orbifolds
  3. Henry de Thélin, Ahlfors’ currents in higher dimension
  4. Erwan Rousseau, Weak analytic hyperbolicity of generic hypersurfaces of high degree in 4
  5. Gerd Dethloff, Steven S.-Y. Lu, Logarithmic Surfaces and Hyperbolicity
  6. Marco Brunella, Courbes entières dans les surfaces algébriques complexes
  7. Daniel Burns, Nessim Sibony, Limit currents and value distribution of holomorphic maps
  8. Luís Gustavo Mendes, Paulo Sad, On dicritical foliations and Halphen pencils
  9. Julie Déserti, Quelques propriétés des transformations birationnelles du plan projectif complexe,

NotesEmbed ?


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.