Kähler manifolds with numerically effective Ricci class
Demailly, Jean-Pierre ; Peternell, Thomas ; Schneider, Michael
Compositio Mathematica, Tome 89 (1993), p. 217-240 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{CM_1993__89_2_217_0,
     author = {Demailly, Jean-Pierre and Peternell, Thomas and Schneider, Michael},
     title = {K\"ahler manifolds with numerically effective Ricci class},
     journal = {Compositio Mathematica},
     volume = {89},
     year = {1993},
     pages = {217-240},
     mrnumber = {1255695},
     zbl = {0884.32023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1993__89_2_217_0}
}

Demailly, Jean-Pierre; Peternell, Thomas; Schneider, Michael. Kähler manifolds with numerically effective Ricci class. Compositio Mathematica, Tome 89 (1993) pp. 217-240. http://gdmltest.u-ga.fr/item/CM_1993__89_2_217_0/

[Au76] Aubin, T.: Equations du type Monge-Ampère sur les variétés kählériennes compactes, C.R. Acad. Sci Paris Ser. A 283 (1976) 119-121; Bull. Sci. Math. 102 (1978) 63-95. | MR 494932 | Zbl 0374.53022

[Be83] Beauville, A.: Variétés Kählériennes dont la première classe de Chern est nulle, J. Diff. Geom. 18 (1983) 755-782. | MR 730926 | Zbl 0537.53056

[Bi63] Bishop, R.: A relation between volume, mean curvature and diameter, Amer. Math. Soc. Not. 10 (1963) 364.

[Bo74a] Bogomolov, F.A.: On the decomposition of Kähler manifolds with trivial canonical class, Math. USSR Sbornik 22 (1974) 580-583. | MR 338459 | Zbl 0304.32016

[Bo74b] Bogomolov, F.A.: Kähler manifolds with trivial canonical class, Izvestija Akad. Nauk 38 (1974) 11-21 and Math. USSR Izvestija 8 (1974) 9-20. | MR 338459 | Zbl 0299.32022

[Ca57] Calabi, E.: On Kähler manifolds with vanishing canonical class, Alg. geometry and topology, Symposium in honor of S. Lefschetz, Princeton Univ. Press, Princeton (1957) 78-89. | MR 85583 | Zbl 0080.15002

[CP91] Campana, F., Peternell, Th.: On the second exterior power of tangent bundles of 3-folds, Comp. Math 83 (1992), 329-346. | Numdam | MR 1175944 | Zbl 0824.14037

[DPS91] Demailly, J.P., Peternell, Th., Schneider, M.: Compact complex manifolds with numerically effective tangent bundles, Preprint 1991. To appear in J. Alg. Geom. | Zbl 0827.14027

[Ga80] Gage, M.E.: Upper bounds for the first eigenvalue of the Laplace-Beltrami operator, Indiana Univ. J. 29 (1980) 897-912. | MR 589652 | Zbl 0465.53031

[Gr81] Gromov, M.: Groups of polynomial growth and expanding maps, Appendix by J. Tits, Publ. I.H.E.S. 53 (1981) 53-78. | Numdam | MR 623534 | Zbl 0474.20018

[Ha77] Hartshorne, R.: Algebraic Geometry, Graduate Texts in Math., Springer, Berlin, 1977. | MR 463157 | Zbl 0367.14001

[HK78] Heintze, E., Karcher, H.: A general comparison theorem with applications to volume estimates for submanifolds, Ann. Scient. Ec. Norm. Sup. 4e Série, 11 (1978) 451-470. | Numdam | MR 533065 | Zbl 0416.53027

[Ka82] Kawamata, Y.: A generalization of Kodaira-Ramanujam's vanishing theorem, Math. Ann. 261 (1982) 43-46. | MR 675204 | Zbl 0476.14007

[KMM87] Kawamata, Y., Matsuki, K., Matsuda, K.: Introduction to the minimal model pro-gram, Adv. Studies Pure Math. 10 (1987) 283-360. | Zbl 0672.14006

[Ko61] Kobayashi, S.: On compact Kähler manifolds with positive definite Ricci tensor, Ann. Math 74 (1961) 570-574. | MR 133086 | Zbl 0107.16002

[Kr86] Kollár, J.: Higher direct images of dualizing sheaves, Ann. Math. 123 (1986) 11-42. | MR 825838 | Zbl 0598.14015

[Li67] Lichnerowicz, A.: Variétés Kählériennes et première classe de Chern, J. Diff. Geom. 1 (1967) 195-224. | MR 226561 | Zbl 0167.20004

[Li71] Lichnerowicz, A.: Variétés Kählériennes à première classe de Chern non négative et variétés riemanniennes à courbure de Ricci généralisée non négative, J. Diff. Geom. 6 (1971) 47-94. | MR 300228 | Zbl 0231.53063

[Li72] Lichnerowicz, A.: Variétés Kählériennes à première classe de Chern non négative et situation analogue dans le cas riemannien, Ist. Naz. Alta Mat., Rome, Symposia Math., vol. 10, Academic Press, New-York (1972) 3-18. | MR 394522 | Zbl 0267.53035

[Ma69] Matsushima, Y.: Recent results on holomorphic vector fields, J. Diff. Geom. 3 (1969) 477-480. | Zbl 0201.25902

[Mi81] Miyanishi, M.: Algebraic methods in the theory of algebraic threefolds, Adv. Studies in Pure Math. 1 (1983) 69-99. | MR 715647 | Zbl 0537.14027

[Mo82] Mori, S.: Threefolds whose canonical bundles are not numerically effective, Ann. Math. 116 (1982) 133-176. | MR 662120 | Zbl 0557.14021

[My41] Myers, S.B.: Riemannian manifolds with positive mean curvature, Duke Math. J. 8 (1941) 401-404. | JFM 67.0673.01 | MR 4518 | Zbl 0025.22704

[Vi82] Viehweg, E.: Vanishing theorems, J. Reine Angew. Math. 335 (1982) 1-8. | MR 667459 | Zbl 0485.32019

[Y77] Yau, S.T.: Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. USA 74 (1977) 1789-1790. | MR 451180 | Zbl 0355.32028

[Y78] Yau, S.T.: On the Ricci curvature of a complex Kähler manifold and the complex Monge-Ampère equation I, Comm. Pure and Appl. Math. 31 (1978) 339-411. | MR 480350 | Zbl 0369.53059