Orbifolds, special varieties and classification theory
- [1] Université Nancy 1, département de mathématiques, BP 239, 54506 Vandoeuvre-les-Nancy (France)
Annales de l’institut Fourier (2004)
- Volume: 54, Issue: 3, page 499-630
- ISSN: 0373-0956
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top- D. Abramovich, Lang's map and Harris conjecture, Isr. J. Math. 101 (1997), 85-91 Zbl0933.14002MR1484870
- D. Arapura, M. Nori, Solvable Fundamental Groups of Algebraic Varieties and Kähler Manifolds, Comp. Math. 116 (1999), 173-193 Zbl0971.14020MR1686777
- D. Barlet, Espace analytique réduit des cycles analytiques complexes compacts d'un espace analytique de dimension finie, LNM 482 (1975), 1-158 Zbl0331.32008MR399503
- W. Barth, C. Peters, A. Van de Ven, Compact Complex Surfaces, Band 4 (1984), Springer Verlag Zbl0718.14023MR749574
- A. Beauville, Annulation du pour les fibrés en droites plats, Proceedings Bayreuth 1989 1507 (1992), 1-15 Zbl0792.14006
- J. Bingener, H. Flenner, On the fibers of analytic mappings, Complex Analysis and Geometry (1993), 45-102, Plenum Press Zbl0792.13005
- S. Bloch, Sur les systèmes de fonctions uniformes satisfaisant l'équation d'une variété algébrique dont l'irrégularité dépasse la dimension, J. Math. Pures et Appliquées 5 (1926), 19-66 Zbl52.0373.04
- F.A. Bogomolov, Holomorphic Tensors and vector Bundles on Projective Varieties, Math. USSR. Izv. 13 (1979), 499-555 Zbl0439.14002
- F.A. Bogomolov, Y. Tschinkel, Density of rational points on elliptic K3 surfaces, Asian Math. J. 4 (2000), 351-368 Zbl0983.14008MR1797587
- F.A. Bogomolov, Y. Tschinkel, Special Elliptic Fibrations Zbl1069.14009
- M. Brunella, Courbes entières dans les surfaces algébriques complexes, Séminaire Bourbaki Exposé 881 (Novembre 2000) Zbl1031.14014
- G. Buzzard, S. Lu, Algebraic surfaces holomorphically dominable by , Inv. Math. 139 (2000), 617-659 Zbl0967.14025MR1738063
- F. Campana, Réduction algébrique d'un morphisme faiblement Kählérien propre et applications, Math. Ann. 256 (1980), 157-189 Zbl0461.32010MR620706
- F. Campana, Coréduction algébrique d'un espace analytique faiblement Kählérien compact, Inv. Math. 63 (1981), 187-223 Zbl0436.32024MR610537
- F. Campana, Réduction d'Albanese d'un morphisme faiblement Kählérien propre et applications I, II, Comp. Math. 54 (1985), 373-416 Zbl0609.32008MR791507
- F. Campana, An application of twistor theory to the non-hyperbolicity of certain compact symplectic Kähler manifolds, J. Reine. Angew. Math 425 (1992) Zbl0738.53037MR1151311
- F. Campana, Connexité rationnelle des variétés de Fano, Ann. Sc. ENS. 25 (1992), 539-545 Zbl0783.14022MR1191735
- F. Campana, Remarques sur le revêtement universel des variétés kählériennes compactes, Bull. S.M.F 122 (1994), 255-284 Zbl0810.32013MR1273904
- F. Campana, Fundamental Group and Positivity Properties of Cotangent Bundles of Compact Kähler Manifolds, J. Alg. Geom. 4 (1995), 487-505 Zbl0845.32027MR1325789
- F. Campana, Negativity of compact curves in infinite étale covers of projective surfaces, J. Alg. Geom. 7 (1998), 673-693 Zbl0951.14009MR1642728
- F. Campana, Ensembles de Green-Lazarsfeld et quotients résolubles des groupes de Kähler, J. Alg. Geom. 10 (2001), 599-622 Zbl1072.14512MR1838973
- F. Campana, Special Varieties and Classification Theory Zbl1059.14047
- F. Campana, Special Varieties and Classification Theory: An overview, Acta Applicandae Mathematicae 75 (2003), 29-49 Zbl1059.14047MR1975557
- F. Campana, Orbifolds, special varieties and classification theory: appendix., Ann. Inst. Fourier 54 (2004), 631-665 Zbl1062.14015MR2097417
- F. Campana, T. Peternell, Complex Threefolds with Non-trivial holomorphic 2-Forms, J. Alg. Geom. 9 (2000), 223-264 Zbl0994.32016MR1735771
- F. Campana, Q. Zhang, Kähler threefolds covered by , (1999)
- J. L. Colliot-Thélène, Arithmétique des variétés rationnelles et problèmes birationnels, Proc. ICM Berkeley (1986), 641-653 Zbl0698.14060MR934267
- J. L. Colliot-Thélène, A. Skorobogatov, P. Swinnerton-Dyer, Double fibers and double covers: paucity in rational points, Acta Arithm. 79 (1997), 113-135 Zbl0863.14011MR1438597
- D. Cox, Mordell-Weil groups of elliptic curves over with , or , Duke Math. J. 49 (1982), 677-689 Zbl0503.14018MR672502
- H. Darmon, A. Granville, On the equations and , Bull. London Math. Soc. 27 (1995), 513-543 Zbl0838.11023MR1348707
- O. Debarre, Higher-Dimensional Algebraic Geometry, (2001), Springer Verlag Zbl0978.14001MR1841091
- J.-P. Demailly, J. El Goul, Hyperbolicity of generic hypersurfaces in the projective 3-space, Amer. J. Math. 122 (2000), 515-546 Zbl0966.32014MR1759887
- J.-P. Demailly, L. Lempert, B. Shiffman, Algebraic approximations of holomorphic maps from Stein domains to projective manifolds, Duke Math. J. 76 (1994), 333-363 Zbl0861.32006MR1302317
- J.-P. Demailly, T. Peternell, M. Schneider, Kähler manifolds with numerically effective Ricci class, Comp. Math. 89 (1993), 217-240 Zbl0884.32023MR1255695
- J.-P. Demailly, T. Peternell, M. Schneider, Compact Kähler Manifolds with hermitian semipositive anticanonical bundle, Comp. Math. 101 (1996), 217-224 Zbl1008.32008MR1389367
- H. Esnault, Classification des variétés de dimension 3 et plus, Séminaire Bourbaki Exposé 568 (1980/81) Zbl0481.14013
- G. Faltings, The general case of S. Lang's Conjecture, The Barsotti Symposium (1994), 175-182, Academic Press, Cambridge Mass Zbl0823.14009
- L. Fong, J. Mc, Kernan, Log Abundance For Surfaces, Flips And Abundance for Algebraic Threefolds 211 (1992), 127-137, Soc. Math. de France Zbl0807.14029
- R. Friedman, J. Morgan, Smooth Four-Manifolds and Complex Surfaces, 27 (1994), Springer Verlag Zbl0817.14017MR1288304
- A. Fujiki, On the Douady Space of a complex space in , Publ. RIMS (1982) Zbl0445.32017
- T. Fujita, On Kähler fibre spaces over curves, J. Math. Soc. Jap. 30 (1978), 779-794 Zbl0393.14006MR513085
- T. Graber, M. Harris, J. Starr, Families of rationally connected varieties, (2001) Zbl1092.14063
- H. Grauert, Jetmetriken und hyperbolische Geometrie, Math. Z. 200 (1989), 149-168 Zbl0664.32020MR978291
- H. Grauert, Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen, Publ. Math. IHES 5 (1960), 1-64 Zbl0100.08001MR121814
- H. Grauert, Mordell’s Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörpern, Publ. Math. IHES 25 (1965), 131-149 Zbl0137.40503MR222087
- M. Hindry, J. Silverman, Diophantine Geometry: an Introduction, 201 (2000), Springer-Verlag Zbl0948.11023MR1745599
- J. Harris, Y. Tschinkel, Rational points on quartics, Duke Math. J. 104 (2000), 477-500 Zbl0982.14013MR1781480
- S. Iitaka, Genera and Classification of Algebraic Varieties, Sugaku 24 (1972), 14-27 Zbl0236.14015MR569689
- S. Iitaka, On Algebraic Varieties whose Universal covering Manifolds are Complex Affine -space, (1973), Tokyo Kunikuniya Zbl0271.14015
- V.A. Kaimanovitch, Brownian Motion and Harmonic Functions on Covering Manifolds. An Entropy Approach., Sov. Math. Dokl. 33 (1986), 812-816 Zbl0615.60074
- Y. Kawamata, On Bloch's Conjecture, Inv. Math. 57 (1980), 97-100 Zbl0569.32012MR564186
- Y. Kawamata, Characterization of Abelian Varieties, Comp. Math. (1981), 253-276 Zbl0471.14022MR622451
- Y. Kawamata, Pluricanonical Forms, Contemp. Math. 241 (1999), 193-209 Zbl0972.14005MR1718145
- Y. Kawamata, E. Viehweg, On a characterization of an Abelian Variety, Comp. Math. 41 (1980), 355-359 Zbl0417.14033MR589087
- Y. Kawamata, K. Matsuda, K. Matsuki, Introduction to the Minimal Model Problem, Adv. Studies in Pure Mathematics 10 (1987), 283-360 Zbl0672.14006MR946243
- S. Keel, S. McKiernan, Rational curves on quasi-projective surfaces, Memoirs AMS 669 (1999) Zbl0955.14031
- S. Kobayashi, Hyperbolic complex spaces, 318 (1998), Springer Verlag Zbl0917.32019MR1635983
- S. Kobayashi, Intrinsic distances, measures and geometric function theory, Bull. AMS 82 (1976), 357-416 Zbl0346.32031MR414940
- S. Kobayashi, T. Ochiai, Meromorphic mappings into compact complex spaces of general type, Inv. Math. 31 (1975), 7-16 Zbl0331.32020MR402127
- J. Kollár, Higher direct image sheaves of dualising sheaves, Ann. Math. 123 (1986), 11-42 Zbl0598.14015MR825838
- J. Kollár, Rational curves on Algebraic varieties, 32 (1996), Springer Verlag Zbl0877.14012MR1440180
- J. Kollár, Shafarevitch maps and plurigenera of Algebraic Varieties, Inv. Math. 113 (1993), 177-215 Zbl0819.14006MR1223229
- J. Kollár, Y. Miyaoka, S. Mori, Rationally connected Varieties, J. Alg. Geom. 1 (1992), 429-448 Zbl0780.14026MR1158625
- J. Kollár, S. Mori, Birational Geometry of Algebraic Varieties, Cambridge Tracts in Mathematics 134 (1998) Zbl0926.14003MR1658959
- S. Lang, Hyperbolic and Diophantine Analysis, Bull. AMS 14 (1986), 159-205 Zbl0602.14019MR828820
- S. Lang, Number Theory III: Diophantine Geometry, vol. 60 (1991), Springer Verlag Zbl0744.14012MR1112552
- S. Lang, A. Néron, Rational points of Abelian Varieties over Function Fields, Amer. J. Math. 81 (1959), 95-118 Zbl0099.16103MR102520
- D. Liebermann, Compactness of the Chow Scheme : Applications to automorphisms and deformations of Kähler Manifolds, 670 (1975), 140-186 Zbl0391.32018
- D. Liebermann, E. Sernesi, Semi-continuity of Kodaira dimension, Bull. Amer. Math. Soc. 81 (1975), 459-460 Zbl0308.14002
- S. Lu, Multiply marked Riemann surfaces and the Kobayashi pseudometric on Algebraic manifolds, Preprint (2001)
- K. Maehara, A finiteness Property of Varieties of General Type, Math. Ann. 262 (1983), 101-123 Zbl0438.14011MR690010
- Y. Manin, Rational Points of Algebraic Curves over Function Fields, Izv. Akad. Nauk. SSSR 27 (1963), 737-756 Zbl0178.55102MR157971
- Y. Miyaoka, On the Kodaira Dimension of Minimal Threefolds, Math. Ann. 281 (1988), 325-332 Zbl0625.14023MR949837
- B. Moishezon, Algebraic Varieties and Compact Complex Spaces, Actes du Congrès International des Mathématiciens, Nice Vol. 2 (1970), 643-648 Zbl0232.14004MR425189
- N. Mok, Factorisation of Semi-Simple Discrete Representations of Kähler Groups, Inv. Math. 110 (1992), 557-614 Zbl0823.53051
- S. Mori, Flip Theorem and the existence of Minimal Models for Threefolds, J. AMS 1 (1988), 117-253 Zbl0649.14023MR924704
- A. Moriwaki, Geometric Height inequality on Varieties with ample cotangent bundle, J. Alg. Geom. 4 (1995), 385-396 Zbl0873.14029MR1311357
- M. Namba, Branched Coverings and Algebraic Functions, 161 (1987), Longman Sc. and Tech. Zbl0706.14017MR933557
- N. Nakayama, Invariance of Plurigenera of algebraic Varieties, (1998) MR1660941
- J. Noguchi, Holomorphic mappings into closed Riemann Surfaces, Hiroshima Math. J. 6 (1976), 281-291 Zbl0338.32017MR422695
- T. Ochiai, On holomorphic curves in algebraic varieties with ample irregularity, Inv. Math. 26 (1976), 83-96 Zbl0374.32006MR473237
- M. Paun, Sur les variétés Kählériennes compactes à classe de Ricci nef, Bull. Sci. Math. 122 (1998), 83-92 Zbl0946.53037MR1613763
- A. N. Parshin, Algebraic Curves over Function Fields, Math. USSR Izv. 2 (1968), 1145-1170 Zbl0188.53003
- E. Peyre, Oral communication, (July 2001)
- M. Raynaud, Flat Modules in algebraic geometry, Comp. Math. 24 (1972), 11-31 Zbl0244.14001MR302645
- H. Swinnerton-Dyer, Applications of Algebraic Geometry to number Theory, Proc. Symp. Pure Math. XX (1969), 1-52 Zbl0228.14001MR337951
- D. Barlet, F. Campana, C. Sabbah, Séminaire: Géometrie Analytique (Deuxième partie), (1982)
- C. Simpson, Subspaces of Moduli Spaces of Rank One Local Systems, Ann. Sc. ENS. 26 (1993), 361-401 Zbl0798.14005MR1222278
- Y.T. Siu, Complex Analyticity of Harmonic Maps, J. Diff. Geom. 17 (1982), 55-138 Zbl0497.32025MR658472
- Y.T. Siu, Invariance of Plurigenera, Inventiones Math. 134 (1998), 661-673 Zbl0955.32017MR1660941
- Y.T. Siu, Extension of Pluricanonical Sections with Plurisubharmonic Weights, (2003), Springer Verlag
- V. Shokurov, 3-fold log-flips, Izv. Akad. Nauk. Ser. Mat. 56 (1992), 105-203 Zbl0785.14023MR1162635
- A. Sommese, A. Van de Ven, Homotopy of Pullback of Varieties, Nagoya Math. J. 102 (1986), 79-90 Zbl0564.14010MR846130
- K. Ueno, Classification Theory of Algebraic Varieties and Compact Complex Manifolds, 439 (1975), Springer Verlag Zbl0299.14007MR506253
- E. Viehweg, Die Additivität der Kodaira Dimension für Projektive Faserräume über Varietäten des Allgemeinen Typs, J. Reine Angew. Math. 330 (1982), 132-142 Zbl0466.14009MR641815
- E. Viehweg, Weak positivity and the additivity of the Kodaira dimension for certain fibre spaces, Vol. I (1983), 329-353, North-Holland Zbl0513.14019
- E. Viehweg, Vanishing theorems and and positivity of Algebraic fibre spaces, J. Proc. Int. Congr. Math. Berkeley (1986) Zbl0685.14013
- C. Voisin, Intrinsic Pseudovolume Forms, (2002)
- Q. Zhang, On projective manifolds with nef anticanonical bundles, J. Reine. Angew. Math. 478 (1996), 57-60 Zbl0855.14007MR1409052
- K. Zuo, Factorisation theorems for representations of fundamental groups of algebraic varieties, (1997)
- H. Grauert, Berichtigung zu der Arbeit 'Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen', Publ. Math., Inst. Hautes Étud. Sci. 16 (1963), 131-132 Zbl0113.29103MR185614
- F. Campana, -connectedness of compact Kähler manifolds. I., Contemp. Math. 241 (1999), 85-96 Zbl0965.32021MR1718138
- K. Zuo, Representations of fundamental groups of algebraic varieties, 1708 (1999), Springer Verlag Zbl0987.14014MR1738433
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