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Hyperplane sections

Part of the Lecture Notes in Mathematics book series (LNM,volume 862)

Keywords

  • Line Bundle
  • Projective Variety
  • Abelian Variety
  • Hyperplane Section
  • Ample Line Bundle

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References

  1. A. Andreotti and T. Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math. 69 (1959), 713–717.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. L. Badescu, On ample divisors, preprint.

    Google Scholar 

  3. R. Bott, On a theorem of Lefschetz, Michigan Math. J. 6 (1959), 211–216.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. G. Castelnuovo, Sulle superficie algebriche le cui sezioni piane curve iperellittiche, Memorie Scelte, Nicola Zanichelli Editore, Bologna, 1937.

    Google Scholar 

  5. G. Castelnuovo and F. Enriques, Sur quelques resultats nouveaux dans la theorie des surfaces algebrique, Note V in P+S below.

    Google Scholar 

  6. F. Enriques, Sur sistemi lineari di superficie algebriche ad intersezioni variabili iperellittiche, Math. Ann. 46 (1895), 179–199.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. T. Fujita, On the hyperplane section principle of Lefschetz, J. Math. Soc. Japan 32 (1980), 153–169.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. T. Fujita, Letter dated January 23, 1980.

    Google Scholar 

  9. R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York, 1977.

    CrossRef  MATH  Google Scholar 

  10. R. Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Math. 156, Springer, Berlin, Heidelberg, New York, 1970.

    MATH  Google Scholar 

  11. R. Hartshorne, Ample vector bundles, Publ. Math. IHES 29 (1966), 63–94.

    MathSciNet  MATH  Google Scholar 

  12. S. Iitaka, "On logarithmic Kodaira dimension of algebraic varieties", Complex Analysis and Algebraic Geometry, ed. W. L. Baily, Jr., and T. Shioda, 175–189, Iwanami Shoten, 1977.

    Google Scholar 

  13. S. Iitaka, Logarithmic forms of algebraic varieties, J. Fac. Sci. Univ. Tokyo Sect. I (IA) 23 (1976), 525–544.

    MathSciNet  MATH  Google Scholar 

  14. M. Nagata, On rational surfaces I, Mem. Coll. Sci. Kyoto (A) 32 (1960), 351–370.

    MathSciNet  MATH  Google Scholar 

  15. E. Picard and G. Simart, Théories des Fonctions Algebriques de Deux Variables Indépendantes, Chelsea Pub. Co., Bronx, New York, 1971.

    MATH  Google Scholar 

  16. L. Roth, On the projective classification of surfaces, Proc. London Math. Soc. (2nd series) 42 (1937), 142–170.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. F. Sakai, "Kodaira dimensions of complements of divisors", Complex Analysis and Algebraic Geometry, ed. W. L. Baily, Jr., and T. Shioda, 240–257, Iwanami Shoten, 1977.

    Google Scholar 

  18. F. Sakai, Canonical models of complements of stable curves, Int. Symp. on Algebraic Geometry at Koyto, 1977, 643–661.

    Google Scholar 

  19. F. Sakai, Logarithmic pluricanonical maps of algebraic surfaces.

    Google Scholar 

  20. J. G. Semple and L. Roth, Introduction to Algebraic Geometry, Clarendon Press, Oxford, 1949.

    MATH  Google Scholar 

  21. A. Silva, Relative vanishing theorems I: applications to ample divisors, Comment. Math. Helv. 52 (1977), 483–489.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. A. J. Sommese, Criteria for quasi-projectivity, Math. Ann. 217 (1975), 247–256, Addendum to "Criteria for quasi-projectivity", Math. Ann. 221 (1976), 95–96.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. A. J. Sommese, On the rationality of the period mapping, Ann. Di Pisa Ser. IV, V (1978), 683–717.

    MathSciNet  MATH  Google Scholar 

  24. A. J. Sommese, Non-smoothable varieties, Comment. Math. Helv. 54 (1979), 140–146.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. A. J. Sommese, On manifolds that cannot be ample divisors, Math. Ann. 221 (1976), 55–72.

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. A. J. Sommese, Hyperplane sections of projective manifolds I — the adjunction mapping, Duke Math. J. 46 (1979), 377–401

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. A. J. Sommese, Submanifolds of Abelian varieties, Math. Ann. 233 (1978), 229–256.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. A. J. Sommese, Concavity Theorems II, preprint.

    Google Scholar 

  29. A. Van de Ven, On the 2-connectedness of very ample divisors on a surface, Duke Math. J. 46 (1979), 403–407.

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. A. Weil, Sur les critères d'équivalence en géométrie algebrique, Math. Ann. 128 (1954), 95–127.

    CrossRef  MathSciNet  MATH  Google Scholar 

  31. A. Weil, Variétés Kählériennes, Hermann, Paris, 1958.

    MATH  Google Scholar 

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© 1981 Springer-Verlag

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Sommese, A.J. (1981). Hyperplane sections. In: Libgober, A., Wagreich, P. (eds) Algebraic Geometry. Lecture Notes in Mathematics, vol 862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090894

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  • DOI: https://doi.org/10.1007/BFb0090894

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10833-7

  • Online ISBN: 978-3-540-38720-6

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