Méthodes L 2 et résultats effectifs en géométrie algébrique
Séminaire Bourbaki : volume 1998/99, exposés 850-864, Astérisque, no. 266 (2000), Talk no. 852, p. 59-90
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     author = {Demailly, Jean-Pierre},
     title = {M\'ethodes $L^2$ et r\'esultats effectifs en g\'eom\'etrie alg\'ebrique},
     booktitle = {S\'eminaire Bourbaki : volume 1998/99, expos\'es 850-864},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {266},
     year = {2000},
     note = {talk:852},
     pages = {59-90},
     zbl = {0962.14014},
     mrnumber = {1772670},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1998-1999__41__59_0}
}
Demailly, Jean-Pierre. Méthodes $L^2$ et résultats effectifs en géométrie algébrique, in Séminaire Bourbaki : volume 1998/99, exposés 850-864, Astérisque, no. 266 (2000), Talk no. 852, pp. 59-90. http://www.numdam.org/item/SB_1998-1999__41__59_0/

[AN54] Y. Akizuki and S. Nakano - Note on Kodaira-Spencer's proof of Lefschetz theorems, Proc. Jap. Acad. 30 (1954), 266-272. | MR 66694 | Zbl 0059.14701

[AS95] U. Angehrn and Y. T. Siu - Effective freeness and point separation for adjoint bundles, Invent. Math. 122 (1995), 291-308. | MR 1358978 | Zbl 0847.32035

[AV65] 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. | Numdam | Numdam | MR 175148 | Zbl 0138.06604

[BeS93] 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. | MR 1211891 | Zbl 0806.14014

[BFS89] M. Beltrametti, P. Francia and A. J. Sommese - On Reider's method and higher order embeddings, Duke Math. J. 58 (1989), 425-439. | MR 1016428 | Zbl 0702.14010

[Boc48] S. Bochner - Curvature and Betti numbers (I) and (II), Ann. of Math. 49 (1948), 379-390; 50 (1949), 77-93. | MR 25238 | Zbl 0039.17603

[Bom70] E. Bombieri - Algebraic values of meromorphic maps, Invent. Math. 10 (1970), 267-287 and Addendum, Invent. Math. 11 (1970), 163-166. | MR 306201 | Zbl 0214.33702

[Bon93] L. Bonavero - Inégalités de Morse holomorphes singulières, C. R. Acad. Sci., Paris, Sér. I 317, n° 12, 1163-1166 (1993) | MR 1257232 | Zbl 0799.32023

[Dem82] J.-P. Demailly - Estimations L 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. | Numdam | Zbl 0507.32021

[Dem85] J.-P. Demailly - Champs magnétiques et inégalités de Morse pour la d ' ' -cohomologie, Ann. Inst. Fourier (Grenoble) 35 (1985), 189-229. | Numdam | MR 812325 | Zbl 0565.58017

[Dem89] J.-P. Demailly - Transcendental proof of a generalized Kawamata-Viehweg vanishing theorem, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989), 123- 126 and: Proceedings of the Conference "Geometrical and algebraical aspects in several complex variables" held at Cetraro, Univ. della Calabria, June (1989). | MR 1004954 | Zbl 01648048

[Dem90] 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). | MR 1178721 | Zbl 0784.32024

[Dem93] J.-P. Demailly - A numerical criterion for very ample line bundles, J. Differential Geom. 37 (1993), 323-374. | MR 1205448 | Zbl 0783.32013

[Dem96] J.-P. Demailly - Effective bounds for very ample line bundles, Invent. Math. 124 (1996), 243-261. | MR 1369417 | Zbl 0862.14004

[Dem98] J.-P. Demailly - Pseudoconvex-concave duality and regularization of currents, Prépublication Institut Fourier, Septembre 1998, 40 p. | MR 1748605

[DK99] J.-P. Demailly, J. Kollár - Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano manifolds, prépublication Institut Fourier 1999.

[DPS94] J.-P. Demailly, Th. Peternell, M. Schneider - Compact complex manifolds with numerically effective tangent bundles, J. Algebraic Geometry 3 (1994) 295-345. | MR 1257325 | Zbl 0827.14027

[DPS98] J.-P. Demailly, Th. Peternell, M. Schneider - Pseudo-effective line bundles on projective varieties, manuscript in preparation (1998).

[Ein94] L. Ein - Note on higher dimensional adjoint linear systems, preprint 1994, personal communication to the author.

[EKL95] L. Ein, O. Küchle And R. Lazarsfeld - Local positivity of ample line bundles, J. Differ. Geom. 42, (1995), 193-219. | MR 1366545 | Zbl 0866.14004

[EL92] L. Ein and R. Lazarsfeld - Seshadri constants on smooth surfaces, Journées de Géométrie Algébrique d'Orsay, Juillet 1992, Astérisque 282 (1993), 177- 186. | MR 1265313 | Zbl 0812.14027

[EL93] 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. | MR 1207013 | Zbl 0803.14004

[EL95] L. Ein and R. Lazarsfeld - Global generation of linear series on terminal threefolds, Intern. J. Math. 6 (1995) 1-18. | MR 1307300 | Zbl 0838.14031

[EV86] H. Esnault and E. Viehweg - Logarithmic De Rham complexes and vanishing theorems, Invent. Math. 86 (1986) 161-194. | MR 853449 | Zbl 0603.32006

[EV92] H. Esnault and E. Viehweg - Lectures on vanishing theorems, DMV Seminar, Band 20, Birkhäuser Verlag (1992). | MR 1193913 | Zbl 0779.14003

[FdB95] G. Fernández Del Busto - Bogomolov instability and Kawamata-Viehweg vanishing, J. Algebr. Geom. 4 (1995) 693-700. | MR 1339844 | Zbl 0846.14005

[FdB96] G. Fernández Del Busto - A Matsusaka-type theorem on surfaces, J. Algebr. Geom. 5 (1996), 513-520. | MR 1382734 | Zbl 0871.14006

[Fuj83] T. Fujita - Semipositive line bundles, J. Fac. Sci. Univ. of Tokyo 30 (1983), 353-378. | MR 722501 | Zbl 0561.32012

[Fuj87] 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. | MR 946238 | Zbl 0659.14002

[Fuj88] T. Fujita - Problem list, Conference held at the Taniguchi Foundation, Katata, Japan, August 1988.

[Fuj93] T. Fujita - Remarks on Ein-Lazarsfeld criterion of spannedness of adjoint bundles of polarized threefolds, preprint 1993.

[Gra60] H. Grauert - Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen, Publ. Math. I.H.E.S. 5 (1960), 5-64. | Numdam | MR 121814 | Zbl 0100.08001

[Gri69] P. A. Griffiths - Hermitian differential geometry, Chern classes and positive vector bundles, Global Analysis, papers in honor of K. Kodaira, PrincetonUniv. Press, Princeton, 1969, 181-251. | MR 258070 | Zbl 0201.24001

[GH78] P. A. Griffiths, J. Harris - Principles of algebraic geometry, Wiley, New York (1978). | MR 507725 | Zbl 0836.14001

[Hel97] S. Helmke - On Fujita's conjecture, Duke Math. J. 88 (1997), 201-231. | MR 1455517 | Zbl 0876.14004

[Hel98] S. Helmke - Global generation of adjoint linear systems, Communication au Congrès d'Oberwolfach "Komplexe Analysis", Septembre 1998. | MR 1686947

[Hir64] H. Hironaka - Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math. 79 (1964) 109-326. | MR 199184 | Zbl 0122.38603

[Hör65] L. Hörmander - L 2 estimates and existence theorems for the ¯ operator, Acta Math. 113 (1965), 89-152. | MR 179443 | Zbl 0158.11002

[Hör66] L. Hörmander - An introduction to Complex Analysis in several variables, 1966, 3rd edition, North-Holland Math. Libr., vol.7, Amsterdam, London (1990). | MR 1045639 | Zbl 0685.32001

[Kaw82] Y. Kawamata - A generalization of Kodaira-Ramanujam's vanishing theorem, Math. Ann. 261 (1982), 43-46. | MR 675204 | Zbl 0476.14007

[Kaw84] Y. Kawamata - The cone of curves of algebraic varieties, Ann. of Math. 119 (1984) 603-633. | MR 744865 | Zbl 0544.14009

[Kaw97a] Y. Kawamata - On Fujita's freeness conjecture for 3-folds and 4-folds, Math. Ann. 308 (1997), 491-505. | MR 1457742 | Zbl 0909.14001

[Kaw97b] Y. Kawamata - Deformation of canonical singularities, alg-geom/9712018 (1997), to appear in J. Amer. Math. Soc. | MR 1631527

[Kaw98] Y. Kawamata - On the extension problem of pluricanonical forms, preprint Univ. of Tokyo at Komaba, September 1998. | MR 1718145

[KMM87] 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. | MR 946243 | Zbl 0672.14006

[Kod53] K. Kodaira - On a differential geometric method in the theory of analytic stacks, Proc. Nat. Acad. Sci. USA 39 (1953), 1268-1273 | MR 66693 | Zbl 0053.11701

[Kod54] K. Kodaira - On Kähler varieties of restricted type, Ann. of Math. 60 (1954), 28-48. | MR 68871 | Zbl 0057.14102

[Kol92] J. Kollár - Effective basepoint freeness, Math. Ann. 296 (1993), 595-605. | MR 1233485 | Zbl 0818.14002

[Kol95] J. Kollár - Singularity of pairs, Preprint University of Utah, November 1995. | MR 1492525

[KoM83] J. Kollár and T. Matsusaka - Riemann-Roch type inequalities, Amer. J. of Math. 105 (1983), 229-252. | MR 692112 | Zbl 0538.14006

[KoMM92] J. Kollár, Y. Miyaoka and S. Mori - Rational connectedness and boundedness of Fano manifolds, J. Differential Geom. 36 (1992), 765-779. | MR 1189503 | Zbl 0759.14032

[Laz93] 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. | MR 1442523 | Zbl 0906.14002

[Lel57] P. Lelong - Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France 85 (1957), 239-262. | Numdam | MR 95967 | Zbl 0079.30901

[Lel69] P. Lelong - Plurisubharmonic functions and positive differential forms, Gordon and Breach, New-York, and Dunod, Paris (1969). | Zbl 0195.11604

[Man93] L. Manivel - Un théorème de prolongement L 2 de sections holomorphes d'un fibré vectoriel, Math. Zeitschrift 212 (1993) 107-122. | MR 1200166 | Zbl 0789.32015

[Mat72] T. Matsusaka - Polarized varieties with a given Hilbert polynomial, Amer. J. of Math. 94 (1972), 1027-1077. | MR 337960 | Zbl 0256.14004

[Mor82] S. Mori - Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982), 133-176. | MR 662120 | Zbl 0557.14021

[Nad89] 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 and Annals of Math., 132 (1990), 549-596. | MR 1078269 | Zbl 0711.53056

[Nak55] S. Nakano - On complex analytic vector bundles, J. Math. Soc. Japan 7 (1955), 1-12. | MR 73263 | Zbl 0068.34403

[Ohs88] T. Ohsawa - On the extension of L 2 holomorphic functions, II, Publ. RIMS, Kyoto Univ. 24 (1988), 265-275. | MR 944862 | Zbl 0653.32012

[OT87] T. Ohsawa and K. Takegoshi - On the extension of L 2 holomorphic functions, Math. Zeitschrift 195 (1987), 197-204. | MR 892051 | Zbl 0625.32011

[Rei88] I. Reider - Vector bundles of rank 2 and linear systems on algebraic surfaces, Ann. of Math. 127 (1988), 309-33.1 | MR 932299 | Zbl 0663.14010

[Rh55] G. De Rham - Variétés différentiables, Hermann, Paris (1955). | Zbl 0065.32401

[Sak88] 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. | MR 1040564 | Zbl 0732.14004

[Sch74] M. Schneider - Ein einfacher Beweis des Verschwindungssatzes für positive holomorphe Vektorraumbündel, Manuscripta Math. 11 (1974), 95-101. | MR 352551 | Zbl 0275.32014

[ShSo85] B. Shiffman, A. J. Sommese - Vanishing theorems on complex manifolds, Progress in Math. no 56, Birkhäuser (1985). | MR 782484 | Zbl 0578.32055

[Sho85] V. Shukorov - The non-vanishing theorem, Math. U.S.S.R. Izv. 19 (1985), 591-607. | Zbl 0605.14006

[Siu74] Y. T. Siu - Analyticity of sets associated to Lelong numbers and the extensionof closed positive currents, Invent. Math. 27 (1974), 53-156. | MR 352516 | Zbl 0289.32003

[Siu93] Y. T. Siu - An effective Matsusaka big theorem, Ann. Inst. Fourier 43 (1993), 1387-1405. | Numdam | MR 1275204 | Zbl 0803.32017

[Siu95] 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; Ann. Math. Stud. 137 (1995), 291-318. | MR 1369144 | Zbl 0853.32035

[Siu96] Y. T. Siu - Effective Very Ampleness, Invent. Math. 124 (1996), 563-571. | MR 1369428 | Zbl 0853.32034

[Siu97] Y. T. Siu - Invariance of Plurigenera, manuscript October 1997, to appear in Inventiones Math. | MR 1660941 | Zbl 0955.32017

[Sko72a] H. Skoda - Sous-ensembles analytiques d'ordre fini ou infini dans n , Bull. Soc. Math. France 100 (1972), 353-408. | Numdam | MR 352517 | Zbl 0246.32009

[Sko72b] H. Skoda - Applications des techniques L 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. | Numdam | MR 333246 | Zbl 0254.32017

[Sko75] H. Skoda - Estimations L 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. | Zbl 0363.32004

[Tsu96] H. Tsuji - Global generation of adjoint bundles, Nagoya Math. J. 142 (1996), 5-16. | MR 1399465 | Zbl 0861.32018

[Vie82] E. Viehweg - Vanishing theorems, J. Reine Angew. Math. 335 (1982), 1-8. | MR 667459 | Zbl 0485.32019