Pseudo-effective line bundles on compact Kähler manifolds

International Journal of Mathematics

Volumn 12, Issue 6, 2001, Pages 689-741

  Demailly, Jean Pierre ^a   Peternell, Thomas ^b   Schneider, Michael ^b  

^a UNIV GRENOBLE ALPES   (France)

^b UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035535802     PISSN: 0129167X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129167X01000861     Document Type: Article

References (59)

1. 1. M. F. Atiyah, Vector bundles over elliptic curves, Proc. London Math. Soc. 27 (1957), 414-452.
2. 2. W. Barth, C. Peters and A. Ven Van de, Compact Complex Surfaces, Ergebnisse der Math. 3. Folge, Band 4, Springer, Berlin, 1984.
3. 3. A. Beauville, Variétés kähleriennes dont la première classe de Chern est nulle, J. Diff. Geom. 18 (1983), 745-782.
4. 4. F. Campana, Coréduction algébrique d'un espace analytique faiblement kählérien compact, Invent. Math. 63 (1981), 187-223.
5. 5. F. Campana, Connexité rationnelle des variétés de Fano, Ann. Sci. ENS 25 (1992), 539-545.
6. 6. F. Campana and Th. Peternell, Towards a Mori theory on compact Kähler 3-folds, I, Math. Nachr. 187 (1997), 29-59.
7. 7. F. Campana and Th. Peternell, Holomorphic 2-forms on complex 3-folds, J. Algebraic Geom. 9 (2000), 223-264.
8. 8. F. Campana, Th. Peternell and Q. Zhang, On the Albanese maps of compact Kähler manifolds with nef anticanonical classes, preprint 1998.
9. 2 pour l'opérateur ∂̄ d'un fibré vectoriel holomorphe semi-positif au-dessus d'une variété kählérienne complète, Ann. Sci. École Norm. Sup. 4e Sér. 15 (1982), 457-511.
10. 10. J.-P. Demailly, Nombres de Lelong généralisés, théorèmes d'intégralité et d'analyticité, Acta Math. 159 (1987), 153-169.
11. 11. J.-P. Demailly, Singular Hermitian metrics on positive line bundles, Proc. Algebraic Geom. Bayreuth 1990; Lecture Notes in Mathematics 1507, Springer-Verlag, 1992, pp. 87-104.
12. 11. J.-P. Demailly, Singular Hermitian metrics on positive line bundles, Proc. Algebraic Geom. Bayreuth 1990; Lecture Notes in Mathematics 1507, Springer-Verlag, 1992, pp. 87-104.
13. 12. J.-P. Demailly, Regularization of closed positive currents and intersection theory, J. Algebraic Geom. 1 (1992), 361-409.
14. 13. J.-P. Demailly, Th. Peternell and M. Schneider, Kähler manifolds with numerically effective Ricci-class, Compositio Math. 89 (1993), 217-240.
15. 14. J.-P. Demailly, Th. Peternell and M. Schneider, Compact complex manifolds with numerically effective tangent bundles, J. Algebraic Geom. 3 (1994), 295-345.
16. 15. J.-P. Demailly, Th. Peternell and M. Schneider, Holomorphic line bundles with partially vanishing cohomology, Israel Math. Conf. Proc. 9 (1996), 165-198.
17. 16. J.-P. Demailly, Th. Peternell and M. Schneider, Compact Kähler manifolds with Hermitian semi-positive anticanonical bundle, Compositio Math. 101 (1996), 217-224.
18. 17. H. Esnault and E. Viehweg, Lectures on Vanishing Theorems, DMV Seminar, Band 20, Birkhäuser Verlag, 1992.
19. 18. G. Fischer and O. Forster, Ein Endlichkeitssatz für Hyperflächen aud kompakten komplexen Räumen, J. für die Reine und Angew. Math. 306 (1979), 88-93.
20. 19. H. Grauert and R. Remmert, Coherent Analytic Sheaves, Grundlehren der Math. Wissenschaften 265, Springer-Verlag, Berlin, 1984.
21. 20. R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer-Verlag, 1977.
22. 21. L. Hörmander, An Introduction to Complex Analysis in Several Variables, 1966, 3rd ed., North-Holland Math. Library 7, Amsterdam, London, 1990.
23. 22. Y. Kawamata, K. Matsuki and K. Matsuda, Introduction to the minimal model program, Adv. Stud. Pure Math. 10 (1987), 283-360.
24. 23. S. Kobayashi, Differential Geometry of Complex Vector Bundles, Princeton University Press, 1987.
25. 24. J. Kollár, Higher direct images of dualizing sheaves I, Ann. Math. 123 (1986), 11-42.
26. 25. J. Kollár, Shafarevich Maps and Plurigenera of Algebraic Varieties, Princeton University Press, 1995.
27. 26. J. Kollár, Rational Curves on Algebraic Varieties, Springer, 1996.
28. 27. J. Kollár, Y. Miyaoka and S. Mori, Rationally connected varieties J. Algebraic Geom. 1 (1992), 429-448.
29. 28. V. A. Krasnov, Compact complex manifolds without meromorphic functions, Mat. Zametki 17 (1975), 119-122 (in Russian).
30. 29. H. Lange and C. Birkenhake, Complex Abelian Varieties, Springer, 1992.
31. 30. P. Lelong, Plurisubharmonic Functions and Positive Differential Forms, Gordon and Breach, New-York, and Dunod, Paris, 1969.
32. 31. B. Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier (Grenoble) 6 (1955-1956), 271-355.
33. 32. Y. Miyaoka, Relative deformations of morphisms and applications to fiber spaces, Comment. Math. University St. Pauli 42 (1993), 1-7.
34. 33. S. Mori, Threefolds whose canonical bundles are not numerically effetive, Ann. Math. 116 (1982), 133-176.
35. 34. S. Mori, Flip theorem and existence of minimal models of 3-folds, J. Amer. Math. Soc. 1 (1988), 177-353.
36. 35. Y. Miyaoka and S. Mori, A numerical criteria for uniruledness, Ann. Math. 124 (1986), 65-69.
37. 36. Ch. Mourougane, Images directes de fibrés en droites adjoints, Publ. Res. Inst. Math. Sci. 33 (1997), 893-916.
38. 37. Ch. Mourougane, Théorèmes d'annulation génériques pour les fibrés vectoriels semi-négatifs, Bull. Soc. Math. France 127 (1999), 115-133.
39. 38. A. M. Nadel, Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature, Proc. Nat. Acad. Sci. USA 86 (1989), 7299-7300 and Ann. Math. 132 (1990), 549-596.
40. 38. A. M. Nadel, Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature, Proc. Nat. Acad. Sci. USA 86 (1989), 7299-7300 and Ann. Math. 132 (1990), 549-596.
41. 39. R. Narasimhan, Introduction to the Theory of Analytic Spaces, Lecture Notes in Mathematics 25, Springer-Verlag, 1966.
42. 40. Y. Namikawa and J. H. M. Steenbrink, Global smoothing of Calabi-Yau 3-folds, Invent. Math. 122 (1995), 403-419.
43. 2 holomorphic functions, Math. Zeitschrift 195 (1987), 197-204.
44. 42. M. Paun, Sur le groupe fondamental des variétés kählériennes compactes à classe de Ricci numériquement effective, C. R. Acad. Sci. 324 (1997), 1249-1254.
45. 43. M. Paun, Sur les variétés kählériennes compactes à classe de Ricci numériquement effective, Bull. Sci. Math. 122 (1998), 83-92.
46. 44. M. Paun, Sur l'effectivité numérique des images inverses de fibrés en droites, Math. Ann. 310 (1998), 411-421.
47. 45. M. Paun, On the Albanese map of compact Kähler manifolds with almost positive Ricci curvature, Prépublication Institut Fourier Grenoble, 1998.
48. 46. Th. Peternell, Minimal varieties with trivial canonical classes. I. Math. Zeitschrift 217 (1994), 377-407.
49. 47. Th. Peternell, Towards a Mori theory on compact Kähler 3-folds, II, Math. Ann. 311 (1998), 729-764.
50. 48. Th. Peternell, Towards a Mori theory on compact Kähler 3-folds, III, Preprint Universität Bayreuth 1999, to appear in Bull. Soc. Math. France.
51. 49. Th. Peternell and F. Serrano, Threefolds with numerical effective anticanonical classes, Collectanea Math. 49 (1998), 465-517.
52. 50. J. Potters, On almost homogeneous compact complex surfaces, Invent. Math. 8 (1969), 244-266.
53. 51. R. Richberg, Stetige streng pseudokonvexe Funktionen, Math. Ann. 175 (1968) 257-286.
54. 52. Y. T. Siu, Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math. 27 (1974), 53-156.
55. n, Bull. Soc. Math. France 100 (1972), 353-408.
56. 54. K. Takegoshi, On cohomology groups of nef line bundles tensorized with multiplier ideal sheaves on compact Kähler manifolds, Osaka J. Math. 34 (1997), 783-802.
57. 55. K. Ueno, Classification theory of algebraic varieties and compact complex spaces, Lecture Notes in Mathematics 439, Springer-Verlag, 1975.
58. 56. K. Ueno, On compact analytic threefolds with non-trivial Albanese tori, Math. Ann. 278 (1987), 41-70.
59. 57. Q. Zhang, On protective manifolds with nef anticanonical bundle, J. Reine Angew. Math. 478 (1996), 57-60.