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When K+(n-4)L fails to be nef

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Abstract

Let X be a smooth complex projective variety of dimension n and let L be an ample line bundle on X. We study polarized pairs (X,L) for which K+(n−3)L is nef but K+(n−4)L fails to be nef.

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References

  1. T. Ando,On extremal rays of the higher dimensional varieties, Inv. Math.81 (1985), 347–357

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Andreatta, E. Ballico, J. Wisniewski,Projective manifolds containing large linear subspaces, Classification of Irregular Varieties, Proceedings Trento 1990, Lecture Notes in Math.1515 (1992), 1–11

    MathSciNet  MATH  Google Scholar 

  3. M. Andreatta, E. Ballico, J. Wisniewski,Vector bundles and adjunction, Intern. J. Math. to appear

  4. M. Beltrametti, M. L. Fania, A. J. Sommese,On the adjunction theoretic classification of projective varieties, Math. Ann.290 (1991), 31–62

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Beltrametti, A. J. Sommese,On the adjunction theoretic classification of polarized varieties, J. reine angew. Math.427 (1992), 157–192

    MathSciNet  MATH  Google Scholar 

  6. T. Fujita,On the structure of polarized varieties with Δ-genera zero, J. Fac. Sci. Univ. Tokyo22 (1975), 103–115

    MathSciNet  MATH  Google Scholar 

  7. T. Fujita,On polarized varieties of small Δ-genera, Tôhoku Math. J.34 (1982), 319–341

    Article  MathSciNet  MATH  Google Scholar 

  8. T. Fujita,On polarized manifolds whose adjoint bundles are not semipositive, Algebraic Geometry, Sendai 1985, Advanced Studies in Pure Math.10 (1987), 171–175

    MathSciNet  MATH  Google Scholar 

  9. T. Fujita,Classification of polarized manifolds of sectional genus two, Algebraic Geometry and Commutative Algebra, in honor of Masayoshi Nagata, Kinokuniya (1987), 73–98

  10. T. Fujita,On singular Del Pezzo varieties, Algebraic Geometry, Proceedings L'Aquila 1988, Lecture Notes in Math.1417 (1990), 117–128

    MathSciNet  MATH  Google Scholar 

  11. P. Ionescu,Generalized adjunction and applications, Math. Proc. Camb. Phil. Soc.99 (1986), 457–472

    Article  MathSciNet  MATH  Google Scholar 

  12. Y. Kawamata,A Generalization of Kodaira-Ramanujam's Vanishing Theorem, Math. Ann.261 (1982), 43–46

    Article  MathSciNet  MATH  Google Scholar 

  13. Y. Kawamata,The cone of curves of algebraic varieties, Ann. of Math.119 (1984), 603–633

    Article  MathSciNet  MATH  Google Scholar 

  14. Y. Kawamata,Small contractions of four dimensional algebraic manifolds, Math. Ann.284 (1984), 595–600

    Article  MathSciNet  MATH  Google Scholar 

  15. Y. Kawamata, K. Matsuda, K. Matsuki,Introduction to the minimal model problem, Algebraic Geometry, Sendai 1985, Advanced Studies in Pure Math.10 (1987), 283–360

    MathSciNet  MATH  Google Scholar 

  16. S. Mori,Threefolds whose canonical bundles are not numerically effective, Ann. of Math.116 (1982), 133–176

    Article  MathSciNet  MATH  Google Scholar 

  17. S. Mori,Threefolds whose canonical bundles are not numerically effective. In, Algebraic Threefolds, Proceedings Varenna 1981, Lecture Notes in Math.947 (1982) 155–189

  18. C. Okonek, M. Schneider, H. Spindler,Vector bundles on complex projective spaces, Progress in Mathematics3 (1980, Birkhauser)

  19. T. Peternell, M. Szurek, J. A. Wisniewski,Numerically effective vector bundles with small Chern classes, Complex Algebraic varieties. Proceedings Bayreuth 1990. Lecture Notes in Math.1507 (1992), 145–156

    MathSciNet  MATH  Google Scholar 

  20. V. V. Shokurov,Theorem on non-vanishing, Math. USSR Izv.26 (1986), 591–604

    Article  MATH  Google Scholar 

  21. A. J. Sommese,On the birational theory of hyperplane sections of projective threefolds, Unpublished manuscript (1981)

  22. A. J. Sommese,On the adjunction theoretic structure of projective varieties, Complex Analysis and Algebraic Geometry. Proceedings Göttingen 1985. Lecture Notes in Math.1194 (1986), 175–213

    MathSciNet  MATH  Google Scholar 

  23. A.J. Sommese,The birational theory of hyperplane sections of projective threefolds. Unpublished manuscript

  24. E. Viehweg,Vanishing theorems, J. reine angew. Math.335 (1982), 1–8

    MathSciNet  MATH  Google Scholar 

  25. J. A. Wisniewski,Length of extremal rays and generalized adjunction, Math. Z.200 (1989), 409–427

    Article  MathSciNet  MATH  Google Scholar 

  26. J. A. Wisniewski,On contractions of extremal rays of Fano manifolds, J. reine angew. Math.417 (1991), 141–157

    MathSciNet  MATH  Google Scholar 

  27. Q. Zhang,Extremal rays on higher dimensional projective varieties, Math. Ann.291 (1991), 497–504

    Article  MathSciNet  MATH  Google Scholar 

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  1. Dipartimento di Matematica, Università di L'Aquila, Via Vetoio Loc. Coppito, I-67100, L'Aquila, Italy

    M. L. Fania

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  1. M. L. Fania
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Fania, M.L. When K+(n-4)L fails to be nef. Manuscripta Math 79, 209–223 (1993). https://doi.org/10.1007/BF02568340

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  • DOI: https://doi.org/10.1007/BF02568340

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