On the adjunction theoretic structure of projective varieties

  • Andrew John Sommese
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1194)


Line Bundle Projective Variety Global Section Hyperplane Section Ample Line Bundle 
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  1. [A+K]
    A. Altman and S. Kleiman, Introduction to Grothendieck Duality Theory, Springer Lecture Notes 146 (1970), Springer Verlag, Berlin.zbMATHGoogle Scholar
  2. [B+P]
    M. Beltrametti and M. Palleschi, On threefolds with low sectional genus, preprint.Google Scholar
  3. [(F+S)1]
    M.L. Fania and A.J. Sommese, On the minimality of hyperplane sections of Gorenstein 3-folds, to appear Proceedings in honor of W. Stoll. Notre Dame (1984), Vieweg.Google Scholar
  4. [(F+S)2]
    M.L. Fania and A.J. Sommese, Varieties whose hyperplane sections are ℙk bundles, preprint.Google Scholar
  5. [F1]
    T. Fujita, On the structure of polarized varieties of Δ genera zero, J. Fac. Sci. Univ. of Tokyo, 22, 103–115 (1975).MathSciNetzbMATHGoogle Scholar
  6. [F2]
    T. Fujita, On the hyperplane section principle of Lefschetz, J. Math. Soc. Japan 32 (1980), 153–169.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [F3]
    T. Fujita, On the structure of Polarized manifolds of total deficiency one, J. Math. Soc. Japan 32 (1980), 709–725.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [F4]
    T. Fujita, Rational retractions onto ample divisors, Sci. Papers of the College of Arts and Sciences of the University of Tokyo 33 (1983), 33–39.MathSciNetzbMATHGoogle Scholar
  9. [F5]
    T. Fujita, Semi-positive line bundles, Jour. Univ. Tokyo, Sect. IA Math. 30 (1983), 353–378.zbMATHGoogle Scholar
  10. [F6]
    T. Fujita, Generalized Adjunction Mappings, preprint of research notice.Google Scholar
  11. [F7]
    T. Fujita, Projective varieties of Δ-genus 1, preprint.Google Scholar
  12. [G+R]
    H. Grauert and O. Riemenschneider, Verschwindungssatze fur analytische Kohomologiegruppen auf komplexen Raumen, Inv. Math. 11 (1970), 263–292.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [Io]
    P. Ionescu, On varieties whose degree is small with respect to codimension, Math. Ann. 271 (1985), 339–348.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [Ka1]
    Y. Kawamata, A generalization of Kodaira-Ramanujam's vanishing theorem, Math. Ann. 261 (1982),43–46.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [Ka2]
    Y. Kawamata, Elementary contractions of algebraic 3-folds, Ann. of Math. 119 (1984), 95–110.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [Ka3]
    Y. Kawamata, The cone of curves of algebraic varieties, Ann. of Math. 119 (1984), 603–633.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [Ke]
    G. Kempf et al., Toroidal embeddings I, Springer Lecture Notes 339 (1973), Springer Verlag, Berlin.zbMATHGoogle Scholar
  18. [L+P]
    A. Lanteri and M. Palleschi, About the adjunction process for polarized algebraic surfaces, J. reine und angew. Math. 352 (1984),15–23.MathSciNetzbMATHGoogle Scholar
  19. [L+S]
    J. Lipman and A.J. Sommese, On the contraction of projective spaces on singular varieties, to appear J. reine und angew. Math.Google Scholar
  20. [M]
    S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982), 133–176.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [Re]
    M. Reid, Canonical 3-folds, Geometric Algebrique d'Angiers (ed. A. Beauville), 273–310, Alphen aan den Rijn Sijthoof and Noordhoff (1980).Google Scholar
  22. [Ro]
    L. Roth, Algebraic Threefolds, Springer-Verlag, Berlin (1953).zbMATHGoogle Scholar
  23. [Sa1]
    F. Sakai, Semi-stable curves on algebraic surfaces and logarithmic pluricanonical maps, Math. Ann. 254, 89–120 (1980).MathSciNetCrossRefzbMATHGoogle Scholar
  24. [Sa2]
    F. Sakai, The structure of normal surfaces, preprint.Google Scholar
  25. [Sa3]
    F. Sakai, Ample Cartier divisors on normal surfaces, preprint.Google Scholar
  26. [Sh+So]
    B. Shiffman and A.J. Sommese. Vanishing Theorems on Complex Manifolds, Progress in Mathematics 56 (1985), Birkhauser, Boston.CrossRefGoogle Scholar
  27. [So1]
    A.J. Sommese, On manifolds that cannot be ample divisors, Math. Ann. 221 (1976), 55–72.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [So2]
    A.J. Sommese, Hyperplane sections of projective surfaces I-The Adjunction Mapping, Duke Math. J., 46 (1979), 377–401.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [So3]
    A.J. Sommese, On the minimality of hyperplane sections of projective threefolds, J. reine und angew. Math. 329 (1981), 16–41.MathSciNetzbMATHGoogle Scholar
  30. [So4]
    A. J. Sommese, Hyperplane sections, Algebraic Geometry, Proceedings Chicago Circle Conference, 1980, Springer Lecture Notes 862 (1981), 232–271.Google Scholar
  31. [So5]
    A.J. Sommese, Ample divisors on 3-folds, Algebraic Threefolds, Springer Lecture Notes 947 (1982), 229–240.Google Scholar
  32. [So6]
    A.J. Sommese, On the birational theory of hyperplane sections of projective threefolds, Unpublished 1981 Manuscript.Google Scholar
  33. [So7]
    A.J. Sommese, Configurations of-2 rational curves on hyperplane sections of projective threefolds, Classification of Algebraic and Analytic Manifolds (ed. K. Ueno), Progress in Mathematics (1983), Birkhauser, Boston.Google Scholar
  34. [So8]
    A.J. Sommese, Ample divisors on normal Gorenstein surfaces, to appear Abh. Math. Hamburg.Google Scholar
  35. [So9]
    A.J. Sommese, Ample divisors on Gorenstein varieties, to appear Proceedings of Complex Geometry Conference, Nancy 1985.Google Scholar
  36. [V]
    E. Viehweg, Vanishing theorems, J. reine und angew. Math. 335 (1982), 1–8.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Andrew John Sommese
    • 1
  1. 1.Department of MathematicsUniversity of Notre DameNotre DameU.S.A.

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