Méthodes L2 et résultats effectifs en géométrie algébrique

Asterisque

Volumn 266, Issue , 2000, Pages 59-90

  Demailly, Jean Pierre ^a  

^a UNIV GRENOBLE ALPES   (France)

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EID: 0012629412     PISSN: 03031179     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article

References (82)

1. Y. Akizuki and S. Nakano - Note on Kodaira-Spencer's proof of Lefschetz theorems, Proc. Jap. Acad. 30 (1954), 266-272.
2. U. Angehrn and Y.T. Siu - Effective freeness and point separation for adjoint bundles, Invent. Math. 122 (1995), 291-308.
3. A. Andreotti and E. Vesentini - Carleman estimates for the Laplace-Beltrami equation in complex manifolds, Publ. Math. I.H.E.S. 25 (1965) 81-130.
4. M. Beltrametti and A.J. Sommese - On k-jet ampleness, Complex Analysis and Geometry, Univ. Series in Math., edited by V. Ancona and A. Silva, Plenum Press, New-York, (1993), 355-376.
5. M. Beltrametti, P. Francia and A.J. Sommese - On Reider's method and higher order embeddings, Duke Math. J. 58 (1989), 425-439.
6. S. Bochner - Curvature and Betti numbers (I) and (II), Ann. of Math. 49 (1948), 379-390;
7. S. Bochner - Ann. of Math. 50 (1949), 77-93.
8. E. Bombieri - Algebraic values of meromorphic maps, Invent. Math. 10 (1970), 267-287
9. and Addendum, Invent. Math. 11 (1970), 163-166.
10. L. Bonavero - Inégalités de Morse holomorphes singulières, C. R. Acad. Sci., Paris, Sér. I 317, no 12, 1163-1166 (1993)
11. 2 pour l'opérateur ∂̄ d'un fibré vectoriel holomorphe semi-positif au-dessus d'une variété kählérienne complète, Ann. Sci. Ec. Norm. Sup. 15 (1982), 457-511.
12. J.-P. Demailly - Champs magnétiques et inégalités de Morse pour la d″ -cohomologie, Ann. Inst. Fourier (Grenoble) 35 (1985), 189-229.
13. J.-P. Demailly - Transcendental proof of a generalized Kawamata-Viehweg vanishing theorem, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989), 123-126
14. and: Proceedings of the Conference "Geometrical and algebraical aspects in several complex variables" held at Cetraro, Univ. della Calabria, June (1989).
15. J.-P. Demailly - Singular hermitian metrics on positive line bundles, Proc. Conf. Complex algebraic varieties (Bayreuth, April 2-6, 1990), edited by K. Hulek, T. Peternell, M. Schneider, F. Schreyer, Lecture Notes in Math., Vol. 1507, Springer-Verlag, Berlin, (1992).
16. J.-P. Demailly - A numerical criterion for very ample line bundles, J. Differential Geom. 37 (1993), 323-374.
17. J.-P. Demailly - Effective bounds for very ample line bundles, Invent. Math. 124 (1996), 243-261.
18. J.-P. Demailly - Pseudoconvex-concave duality and regularization of currents, Prépublication Institut Fourier, Septembre 1998, 40p.
19. J.-P. Demailly, J. Kollár - Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano manifolds, prépublication Institut Fourier 1999.
20. J.-P. Demailly, Th. Peternell, M. Schneider - Compact complex manifolds with numerically effective tangent bundles, J. Algebraic Geometry 3 (1994)7 295-345.
21. J.-P. Demailly, Th. Peternell, M. Schneider - Pseudo-effective line bundles on projective varieties, manuscript in preparation (1998).
22. L. Ein - Note on higher dimensional adjoint linear systems, preprint 1994, personal communication to the author.
23. L. Ein, O. Küchle and R. Lazarsfeld - Local positivity of ample line bundles, J. Differ. Geom. 42, (1995), 193-219.
24. L. Ein and R. Lazarsfeld - Seshadri constants on smooth surfaces, Journées de Géométrie Algébrique d'Orsay, Juillet 1992, Astérisque 282 (1993), 177-186.
25. L. Ein and R. Lazarsfeld - Global generation of pluricanonical and adjoint linear series on smooth projective threefolds, Jour. of Am. Math. Soc. 6 (1993), 875-903.
26. L. Ein and R. Lazarsfeld - Global generation of linear series on terminal threefolds, Intern. J. Math. 6 (1995) 1-18.
27. H. Esnault and E. Viehweg - Logarithmic De Rham complexes and vanishing theorems, Invent. Math. 86 (1986) 161-194.
28. H. Esnault and E. Viehweg - Lectures on vanishing theorems, DMV Seminar, Band 20, Birkhäuser Verlag (1992).
29. G. Fernández del Busto - Bogomolov instability and Kawamata-Viehweg vanishing, J. Algebr. Geom. 4 (1995) 693-700.
30. G. Fernández del Busto - A Matsusaka-type theorem on surfaces, J. Algebr. Geom. 5 (1996), 513-520.
31. T. Fujita - Semipositive line bundles, J. Fac. Sci. Univ. of Tokyo 30 (1983), 353-378.
32. T. Fujita - On polarized manifolds whose adjoint bundles are not semipositive, Algebraic Geometry, Sendai, 1985, Adv. Stud, in Pure Math., Vol. 10, North Holland, T. Oda (ed.) (1987), 167-178.
33. T. Fujita - Problem list, Conference held at the Taniguchi Foundation, Katata, Japan, August 1988.
34. T. Fujita - Remarks on Ein-Lazarsfeld criterion of spannedness of adjoint bundles of polarized threefolds, preprint 1993.
35. H. Grauert - Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen, Publ. Math. I.H.E.S. 5 (1960), 233-292.
36. P.A. Griffiths - Hermitian differential geometry, Chern classes and positive vector bundles, Global Analysis, papers in honor of K. Kodaira, Princeton Univ. Press, Princeton, 1969, 181-251.
37. P.A. Griffiths, J. Harris - Principles of algebraic geometry, Wiley, New York (1978).
38. S. Helmke - On Fujita's conjecture, Duke Math. J. 88 (1997), 201-231.
39. S. Helmke - Global generation of adjoint linear systems, Communication au Congrès d'Oberwolfach "Komplexe Analysis", Septembre 1998.
40. H. Hironaka - Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math. 79 (1964) 109-326.
41. 2 estimates and existence theorems for the ∂̄ operator, Acta Math. 113 (1965), 89-152.
42. L. Hörmander - An introduction to Complex Analysis in several variables, 1966, 3rd edition, North-Holland Math. Libr., vol.7, Amsterdam, London (1990).
43. Y. Kawamata - A generalization of Kodaira-Ramanujam's vanishing theorem, Math. Ann. 261 (1982), 43-46.
44. Y. Kawamata - The cone of curves of algebraic varieties, Ann. of Math. 119 (1984) 603-633.
45. Y. Kawamata - On Fujita's freeness conjecture for 3-folds and 4-folds, Math. Ann. 308 (1997), 491-505.
46. Y. Kawamata - Deformation of canonical singularities, alg-geom/9712018 (1997), to appear in J. Amer. Math. Soc.
47. Y. Kawamata - On the extension problem of pluricanonical forms, preprint Univ. of Tokyo at Komaba, September 1998.
48. Y. Kawamata, K. Matsuda and K. Matsuki - Introduction to the minimal problem Algebraic Geometry, Sendai, 1985, Adv. Stud. in Pure Math., Vol. 10, T. Oda (ed.), North Holland, Amsterdam (1987), 283-360.
49. K. Kodaira - On a differential geometric method in the theory of analytic stacks, Proc. Nat. Acad. Sci. USA 39 (1953), 1268-1273
50. K. Kodaira - On Kähler varieties of restricted type, Ann. of Math. 60 (1954), 28-48.
51. J. Kollár - Effective basepoint freeness, Math. Ann. 296 (1993), 595-605.
52. J. Kollár - Singularity of pairs, Preprint University of Utah, November 1995.
53. J. Kollár and T. Matsusaka - Riemann-Roch type inequalities, Amer. J. of Math. 105 (1983), 229-252.
54. J. Kollár, Y. Miyaoka and S. Mori - Rational connectedness and boundedness of Fano manifolds, J. Differential Geom. 36 (1992), 765-779.
55. R. Lazarsfeld, - Lectures on linear series, with the assistance of G. Fernández del Busto, Lectures of a summer program on Complex Algebraic Geometry, Park City, 1993, Amer. Math. Soc., IAS/Park City Math. Ser. 3 (1997), 163-219.
56. P. Lelong - Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France 85 (1957), 239-262.
57. P. Lelong - Plurisubharmonic functions and positive differential forms, Gordon and Breach, New-York, and Dunod, Paris (1969).
58. 2 de sections holomorphes d'un fibré vectoriel, Math. Zeitschrift 212 (1993) 107-122.
59. T. Matsusaka - Polarized varieties with a given Hilbert polynomial, Amer. J. of Math. 94 (1972), 1027-1077.
60. S. Mori - Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982), 133-176.
61. A.M. Nadel - Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature, Proc. Nat. Acad. Sci. U.S.A. 86 (1989), 7299-7300
62. and Annals of Math., 132 (1990), 549-596.
63. S. Nakano - On complex analytic vector bundles, J. Math. Soc. Japan 7 (1955), 1-12.
64. 2 holomorphic functions, II, Publ. RIMS, Kyoto Univ. 24 (1988), 265-275.
65. 2 holomorphic functions, Math. Zeitschrift 195 (1987), 197-204.
66. I. Reider - Vector bundles of rank 2 and linear systems on algebraic surfaces, Ann. of Math. 127 (1988), 309-33.1
67. G. De Rham - Variétés différentiables, Hermann, Paris (1955).
68. F. Sakai - Reider-Serrano's method on normal surfaces, Proc. Intern. Conf. on Algebraic Geometry (L'Aquila, June 1988), Lecture Notes in Math., Vol. 1417, Springer-Verlag, Berlin, 1990, 301-319.
69. M. Schneider - Ein einfacher Beweis des Verschwindungssatzes für positive holomorphe Vektorraumbündel, Manuscripta Math. 11 (1974), 95-101.
70. B. Shiffman, A.J. Sommese - Vanishing theorems on complex manifolds, Progress in Math. no 56, Birkhäuser (1985).
71. V. Shukorov - The non-vanishing theorem, Math. U.S.S.R. Izv. 19 (1985), 591-607.
72. Y.T. Siu - Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math. 27 (1974), 53-156.
73. Y.T. Siu - An effective Matsusaka big theorem, Ann. Inst. Fourier 43 (1993), 1387-1405.
74. Y.T. Siu - Very ampleness criterion of double adjoint of ample line bundles, Princeton Conf. in honor of Robert C. Gunning and Joseph J. Kohn, Princeton University, NJ, USA, Mar. 16-20, 1992;
75. Ann. Math. Stud. 137 (1995), 291-318.
76. Y.T. Siu - Effective Very Ampleness, Invent. Math. 124 (1996), 563-571.
77. Y.T. Siu - Invariance of Plurigenera, manuscript October 1997, to appear in Inventiones Math.
78. n, Bull. Soc. Math. France 100 (1972), 353-408.
79. 2 à la théorie des idéaux d'une algèbre de fonctions holomorphes avec poids, Ann. Scient. Ec. Norm. Sup. 4e Série 5 (1972), 545-579.
80. 2 pour l'opérateur ∂̄ et applications arithmétiques, Séminaire P. Lelong (Analyse), année 1975/76, Lecture Notes in Math., Vol. 538, Springer-Verlag, Berlin (1977), 314-323.
81. H. Tsuji - Global generation of adjoint bundles, Nagoya Math. J. 142 (1996), 5-16.
82. E. Viehweg - Vanishing theorems, 3. Reine Angew. Math. 335 (1982), 1-8.