Variétés de Fano

Olivier Debarre

Séminaire Bourbaki (1996-1997)

  • Volume: 39, page 197-221
  • ISSN: 0303-1179

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Debarre, Olivier. "Variétés de Fano." Séminaire Bourbaki 39 (1996-1997): 197-221. <http://eudml.org/doc/110229>.

@article{Debarre1996-1997,
author = {Debarre, Olivier},
journal = {Séminaire Bourbaki},
keywords = {Fano varieties; deformation types; rational connectedness of Fano varieties},
language = {fre},
pages = {197-221},
publisher = {Société Mathématique de France},
title = {Variétés de Fano},
url = {http://eudml.org/doc/110229},
volume = {39},
year = {1996-1997},
}

TY - JOUR
AU - Debarre, Olivier
TI - Variétés de Fano
JO - Séminaire Bourbaki
PY - 1996-1997
PB - Société Mathématique de France
VL - 39
SP - 197
EP - 221
LA - fre
KW - Fano varieties; deformation types; rational connectedness of Fano varieties
UR - http://eudml.org/doc/110229
ER -

References

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  1. [AS] U. Angehrn, Y.-T. Siu - Effective Freeness and Point Separation, Invent. Math.122 (1995), 291-308. Zbl0847.32035MR1358978
  2. [B] V. Batyrev - Boundedness of the degree of multidimensional toric Fano varieties (en russe avec résumé anglais), Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1982) 22-27, 76-77; trad. anglaise : Moscow Univ. Math. Bull.37 (1982), 28-33. Zbl0505.14033MR650598
  3. [Be] A. Besse - Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete10, Springer-Verlag, Berlin-New York, 1987. Zbl0613.53001MR867684
  4. [BC] A. Bishop, R. Crittenden - Geometry of Manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete10, Academic Press, New York and London, 1964. Zbl0132.16003MR169148
  5. [Bo] F. Bogomolov - Holomorphic tensors and vector bundles on projective manifolds (en russe), Izv. Akad. Nauk SSSR Ser. Mat.42 (1978), 1227-1287, 1439; trad. anglaise : Math. USSR Izvestiya13 (1979), 499-555. Zbl0439.14002MR522939
  6. [Bor] A. Borel - Linear algebraic groups. Benjamin, 1969. Zbl0186.33201MR251042
  7. [Bou] J.-P. Bourguignon - Premières formes de Chern des variétés kählériennes compactes, d'après E. Calabi, T. Aubin et S. T. Yau, Séminaire Bourbaki, vol. 1977/78, Exp. 507, 1-21, SpringerLectures Notes710, Springer Verlag, 1979. Zbl0413.53035MR554212
  8. [C1] F. Campana - Connexité rationnelle des variétés de Fano, Ann. Sc. Ec. Norm. Sup.25 (1992), 539-545. Zbl0783.14022MR1191735
  9. [C2] F. Campana - Coréduction algébrique d'un espace analytique compact faiblement kählérien, Invent. Math.63 (1981), 187-223. Zbl0436.32024MR610537
  10. [C3] F. Campana - Remarques sur le revêtement universel des variétés kählériennes compactes, Bull. Soc. Math. Fr.122 (1994), 255-284. Zbl0810.32013MR1273904
  11. [C4] F. Campana - Une version géométrique généralisée du théorème du produit de Nadel, Bull. Soc. Math. Fr.119 (1991), 479-493. Zbl0783.14023MR1136848
  12. [Ca] F. Catanese - Chow varieties, Hilbert schemes and moduli spaces of surfaces of general type, J. Alg. Geom.1 (1992), 561-596. Zbl0807.14006MR1174902
  13. [CT] J.-L. Colliot-Thélène - Arithmétique des variétés rationnelles et problèmes bimtionnels, Proc. Int. Congr. Math., (Berkeley, Calif., 1986), 641-653, A.M.S., Providence, RI, 1987. Zbl0698.14060MR934267
  14. [D] J.-P. Demailly - A numerical criterion for very ample line bundles, J. Diff. Geom.37 (1993), 323-374. Zbl0783.32013MR1205448
  15. [De] M. Demazure - Caractérisations de l'espace projectif, d'après S. Mori, Séminaire Bourbaki, vol. 1979/80, Exp. 544, 11-19, SpringerLectures Notes842, Springer Verlag, 1981. Zbl0469.14008MR636514
  16. [F] G. Fano - Sulle varietà algebriche a tre dimensione aventi tutti i generi nulli, Atti Congr. Internaz. di Matematica, Bologna4 (1931), 115-119. JFM57.0448.03
  17. [Fu] A. Fujiki - Deformation of uni-ruled manifolds, Publ. RIMSKyoto Univ.17 (1981), 687-702. Zbl0509.32011MR642656
  18. [G] A. Grothendieck - Fondements de la géométrie algébrique. Extraits du Séminaire Bourbaki, 1957-1962, Sec. Math., Paris, 1962. Réédition Astérisque hors série 5, Soc. Math. Fr., 1997. Zbl0239.14002MR146040
  19. [I1] V. Iskovskikh - Fano 3-folds I (en russe), Izv. Akad. Nauk SSSR Ser. Mat.41 (1977), 516-562, 717; trad. anglaise : Math. USSR Izvestiya11 (1977), 485-527. Zbl0382.14013MR463151
  20. [12] V. Iskovskikh - Fano 3-folds II (en russe), Izv. Akad. Nauk SSSR Ser. Mat.42 (1978), 506-549; trad. anglaise : Math. USSR Izvestiya12 (1978), 469-506. Zbl0424.14012MR503430
  21. [Ka] Y. Kawamata - Boundedness of Q-Fano threefolds, Proceedings of the International Conference on Algebra, (Novosibirsk, 1989), 439-445, Contemp. Math.131, Part 3, A.M.S., Providence, RI, 1992. Zbl0785.14024MR1175897
  22. [K1] J. Kollár - Rational Curves on Algebraic Varieties. Ergebnisse der Mathematik und ihrer Grenzgebiete32, Springer Verlag, Berlin, 1996. Zbl0877.14012MR1440180
  23. [K2] J. Kollár - Effective Base Point Freeness, Math. Ann. 296 (1993), 595-605. Zbl0818.14002MR1233485
  24. [K3] J. Kollár - Shafarevich maps and automorphic forms. M. B. Porter Lectures, Princeton University Press, Princeton, NJ, 1995. Zbl0871.14015MR1341589
  25. [K4] J. Kollár - Shafarevich maps and plurigenera of algebraic varieties, Invent. Math.113 (1993), 177-215. Zbl0819.14006MR1223229
  26. [KM] J. Kollár, T. Matsusaka — Riemann-Roch type inequalities, Amer. J. Math.105 (1983), 229-252. Zbl0538.14006MR692112
  27. [KMM1] J. Kollár, Y. Miyaoka, S. Mori - Rational Curves on Fano Varieties, Proc. Alg. Geom. Conf. Trento, 100-105, SpringerLecture Notes1515, Springer Verlag, 1992. Zbl0776.14012MR1180339
  28. [KMM2] J. Kollár, Y. Miyaoka, S. Mori - Rationally Connected Varieties, J. Alg. Geom.1 (1992), 429-448. Zbl0780.14026MR1158625
  29. [KMM3] J. Kollár, Y. Miyaoka, S. Mori - Rational Connectedness and Boundedness of Fano Manifolds, J. Diff. Geom.36 (1992), 765-769. Zbl0759.14032MR1189503
  30. [LBS] C. Lebrun, S. Salamon - Strong ridigity of positive quaternion-Kähler manifolds, Invent. Math.118 (1994), 109-132. Zbl0815.53078MR1288469
  31. [Le] M. Levine - Deformation of uni-ruled varieties, Duke Math. J.48 (1981), 467-473. Zbl0485.14011MR620260
  32. [M] Y. Manin - Cubic forms. Algebra, geometry, arithmetic. Second edition. North-HollandMathematical Library, 4. North-Holland Publishing Co., Amsterdam-New York, 1986. Zbl0582.14010MR833513
  33. [Ma] T. Matsusaka - On canonically polarized varieties (II), Amer. J. Math.92 (1970), 283-292. Zbl0195.22802MR263816
  34. [Me] G. Megyesi - Fano threefolds in positive characteristic, à paraître dans J. Alg. Geom. Zbl0959.14026
  35. [Mo] S. Mori - Projective manifolds with ample tangent bundles, Ann. of Math.110 (1979), 593-606. Zbl0423.14006MR554387
  36. [MM] S. Mori, S. Mukai - Classification of Fano threefolds with b2 ≥ 2, Manuscr. Math.36 (1981), 147-162. Zbl0478.14033
  37. [N] A. Nadel - The boundedness of degree of Fano varieties with Picard number 1, J. Amer. Math. Soc.4 (1991), 681-692. Zbl0754.14026MR1115788
  38. [S] J.-P. Serre - Cohomologie Galoisienne. SpringerLecture Notes5, Springer Verlag, Berlin, 1964. Zbl0136.02801
  39. [SB] N. Shepherd-Barron - Fano threefolds in positive characteristic, Comp. Math. 105 (1997), 237-265. Zbl0889.14021MR1440723
  40. [Sh] V.V. Shokurov - The existence of a line on Fano varieties (en russe), Izv. Akad. Nauk SSSR Ser. Mat.43 (1979) 922-964, 968; trad. anglaise : Math. USSR Izvestiya14 (1980), 395-405. Zbl0422.14019MR548510
  41. [T] H. Tsuji - Global generation of adjoint bundles, Nagoya. Math. J.142 (1996), 5-16. Zbl0861.32018MR1399465
  42. [Y1] S.T. Yau - On Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sc. USA74 (1977), 1798-1799. Zbl0355.32028MR451180
  43. [Y2] S.T. Yau - On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation, I, Comm. Pure and Appl. Math.31 (1978), 339-411. Zbl0369.53059MR480350

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