Hyperplane sections and deformations

  • Lucian BĂdescu
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1056)


Exact Sequence Vector Bundle Line Bundle Elliptic Curve Complete Intersection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Artin, Algebraic approximation of structures over complete local rings, Publ. Math. IHES No. 36 (1969) 23–58.Google Scholar
  2. 2.
    M. Artin, On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966) 129–136.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    L. BĂdescu, On ample divisors, Nagoya Math. J. 86 (1982) 155–171.MathSciNetzbMATHGoogle Scholar
  4. 4.
    L. BĂdescu, On ample divisors:II, Proceedings of the Week of Algebraic Geometry, Bucharest 1980, Teubner-Texte Math. Band 40, Leipzig 1981.Google Scholar
  5. 5.
    L. BĂdescu, The projective plane blown up at a point as an ample divisor, Atti Accad. Ligure Scienze Lettere, 38 (1981) 3–7.MathSciNetGoogle Scholar
  6. 6.
    C. BĂnicĂ, Sur les fibres infinitesimalles d'un morphisme propre d'espaces complexes, Séminaire F. Norguet No. IV, Springer Lecture Notes in Math. 807 (1980).Google Scholar
  7. 7.
    C. BĂnicĂ-O. StĂnĂşilĂ, Algebraic Methods in the Global Theory of Complex Spaces, John Wiley, New York (1976).zbMATHGoogle Scholar
  8. 8.
    E. Bombieri-D. Husemoller, Classification and embeddings of surfaces, Proc. Symp. Pure Math. 29 (1975) 329–420.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    L. Brenton, On singular complex surfaces with negative canonical bundle, with applications to singular compactification of C2 and 3-dimensional rational singularities, Math. Ann. 248 (1980) 117–124.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    A. Buium, Weighted projective spaces as ample divisors, Revue Roum. Math. Pur. Appl. 26 (1981) 833–842.MathSciNetzbMATHGoogle Scholar
  11. 11.
    M. Demazure, Surfaces de Del Pezzo, in Springer Lecture Notes Math 777 (1980).Google Scholar
  12. 12.
    I. Dolgachev, Weighted projective varieties, in Springer Lecture Notes Math. 956 (1982).Google Scholar
  13. 13.
    L. de Fiore, S. Freni, Sulle varietà segate dagli iperpiani in varietà di Grassmann di indici qualunque, Preprint, Napoli (1980).Google Scholar
  14. 14.
    T. Fujita, Impossibility oriterion of being an ample divisor, J. Math. Soc. Japan 34 (1982) 355–363.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    T. Fujita, Vector bundles on ample divisors, J. Math. Soc. Japan 33 (1981) 405–414.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    T. Fujita, On the hyperplane section principle of Lefschetz, J. Math. Soc. Japan, 32 (1980) 153–169.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    T. Fujita, On the structure of polarized manifolds with total deficiency one, I, J. Math. Soc. Japan 32 (1980) 709–725.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    M.H. Gizatullin, On affine surfaces that can be completed by a non-singular rational curve, Izv. Akad. Nauk USSR 34 (1970) 787–810.MathSciNetzbMATHGoogle Scholar
  19. 19.
    A. Grothendieck-J. Dieudonné, Eléments de Géométrie Algebrique, Chap. II, III, IV, Publ. Math. IHES, Bures sur Yvette.Google Scholar
  20. 20.
    A. Grothendieck, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux, North Holland, Amsterdam (1968).zbMATHGoogle Scholar
  21. 21.
    R. Hartshorne, Algebraic Geometry, Springer Verlag (1977).Google Scholar
  22. 22.
    R. Hartshorne, Curves with high self-intersection on algebraic surfaces, Publ. Math. IHES No. 36 (1969) 111–125.Google Scholar
  23. 23.
    R. Hartshorne, Topological conditions for smoothing algebraic singularities, Topology 13 (1974) 241–253.MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    F. Hidaka-K. Watanabe, Normal Gorenstein surfaces with ample anti-canonical divisor, Tokyo J. Math,, 4 (1981) 319–330.MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    P. Ionescu, Deformations of complete intersections, Revue Roum. Math. Pur. Appl. 25 (1980) 751–758.MathSciNetzbMATHGoogle Scholar
  26. 26.
    V.A. Iskovskih, Fano 3-folds, Math. USSR Izvest. 11 (1977) 485–527.MathSciNetCrossRefGoogle Scholar
  27. 27.
    G. Kempf, Vanishing theorems for flag manifolds, Amer. J. Math. 98 (1976) 325–331.MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    S. Mori, On a generalization of complete intersections, J. Math. Kyoto Univ. 15 (1975) 619–646.MathSciNetzbMATHGoogle Scholar
  29. 29.
    D. Mumford, Varieties defined by quadratic equations, CIME (1969) 29–100 (Roma, Ediz. Cremonese).Google Scholar
  30. 30.
    D. Mumford, A remark on a paper of Schlessinger, Rice Univ. Studies 59 (1) (1973) 113–117.MathSciNetzbMATHGoogle Scholar
  31. 31.
    M. Nagata, On rational surfaces, I, Mem. Coll. Sci. Kyoto (A) 32 (1960) 351–370.MathSciNetzbMATHGoogle Scholar
  32. 32.
    H. Pinkham, Deformations of algebraic varieties with Gm-action, Astérisque 20, Société Math. de France (1974).Google Scholar
  33. 33.
    M. Schlessinger, On rigid singularities, Rice Univ. Studies 59 (1) (1973) 147–162.MathSciNetzbMATHGoogle Scholar
  34. 34.
    G. Scorza, Sopra una certa classe di varietà razionali, Rend. Circ. Matem. Palermo 28 (1909) 400–401.CrossRefzbMATHGoogle Scholar
  35. 35.
    E. Sernesi, Small deformations of global complete intersections, Boll. Un. Matem. Ital. (4) 12 (1975) 138–146.MathSciNetzbMATHGoogle Scholar
  36. 36.
    A.J. Sommese, Non-smoothable varieties, Comment. Math. Helv. 54 (1979) 140–146MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    A.J. Sommese, On manifolds that cannot be ample divisors, Math. Ann. 221 (1976) 55–72.MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    ***, Correspondence, Amer. J.Math. 79 (1957) 951–952 (=A. Weil, Oeuvres sc. II 555–556).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Lucian BĂdescu
    • 1
  1. 1.Dept. of MathematicsIncrest BucharestBucharestRumania

Personalised recommendations