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On projective varieties with nef anticanonical divisors

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References

  1. Boucksom, S.: On the volume of a big line bundle. Intern. J. Math 13, 1043–1063 (2002)

    Article  Google Scholar 

  2. Boucksom, S., Demailly, J., Paun, M., Peternell, T.: The pseudo-effective cone of a compact Kähler manifolds and varieties of negative Kodaira dimension. math.AG/0405285 (2004)

  3. Campana, F.: Connexité rationnelle des variétés de Fano. Ann. Sci. E.N.S 25, 539–545 (1992)

    Google Scholar 

  4. Campana, F.: Orbifolds, Special Varieties and Classification Theory. Ann. Inst. Fourier, Grenoble 54(3), 499–630 (2004) /math.AG/0110051(2001)

    Google Scholar 

  5. Bauer, T., Campana, F., Eckl, T ., Kebekus, S., Peternell, T., Rams, S., Szemberg, T., Wotzlaw, L.: A reduction map for nef line bundles. Collection of papers dedicated to Hans Grauert, Springer-Verlag (2002), 27–36.(math.AG/0106147)

  6. Demailly, J., Peternell, T., Schneider, M.: Compact Kähler manifolds with Hermitian semi-positive anticanonical bundle. Compositio. Math 101, 217–224 (1996)

    Google Scholar 

  7. Graber, H. T., Harris, J., Starr, J.: Families of rationally connected varieties. J. Amer. Math. Soc. 16(1), 57–67 (2003)

    Article  Google Scholar 

  8. Kawamata, Y.: Characterization of abelian varieties. Comp. Math. 43, 253–276 (1981)

    Google Scholar 

  9. Kawamata, Y.: Subadjunction of log canonical divisors. II Amer.J. Math. 120(5), 893–899 (1998)

    Google Scholar 

  10. Kawamata, Y., Matsuada, K., Matsuki, K.: Introduction to the minimal Model Problem. Adv. Stud. Pure. Math. 10, 283–360 (1987)

    Google Scholar 

  11. Kollár, J., Miyaoka, Y., Mori, S.: Rationally connected varieties. J. Alg. Geom. 1, 429–448 (1992)

    Google Scholar 

  12. Lu, S.: A refined Kodaira dimension and its canonical fibration. math.AG/0211029 (2002)

  13. Miyaoka, Y., Mori, S.: A numerical criterion for uniruledness. Ann. of Math. 124, 65–69 (1986)

    Google Scholar 

  14. Nakayama, N.: Zariski-Decomposition and Abundance. RIMS-1142 (1997 )

  15. Peternell, T., Serrano, F.: Threefolds with numerically effective anticanonical class. Collectanea Math 49, 465–517 (1998)

    Google Scholar 

  16. Tsuji, H.: Numerical trivial fibration. math.AG/0001023 (2000)

  17. Viehweg, E.: Weak positivity and the additivity of Kodaira dimension for certain fiber spaces. Adv. Stud. Pure. Math 1 1, 329–353 (1983)

    Google Scholar 

  18. Zhang, Q.: On projective manifolds with nef anticanonical bundles. J. reine angew. Math. 478, 57–60 (1996)

    Google Scholar 

  19. Zhang, Q.: Rational connectedness of log Q-Fano varieties. math.AG/0408301 (to appear in J. reine angew. Math)

  20. McKernan, J., Prokhorov, Y.: Threefold Thresholds. math.AG/0304152 (2003)

  21. Bauer, T., Peternell, T.: Nef reduction and anticanonical bundles. math.AG/0310484 (2003)

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Zhang, Q. On projective varieties with nef anticanonical divisors. Math. Ann. 332, 697–703 (2005). https://doi.org/10.1007/s00208-005-0649-z

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  • DOI: https://doi.org/10.1007/s00208-005-0649-z

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