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Hyperplane sections and deformations

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Algebraic Geometry Bucharest 1982

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1056))

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References

  1. M. Artin, Algebraic approximation of structures over complete local rings, Publ. Math. IHES No. 36 (1969) 23–58.

    Google Scholar 

  2. M. Artin, On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966) 129–136.

    Article  MathSciNet  MATH  Google Scholar 

  3. L. BĂdescu, On ample divisors, Nagoya Math. J. 86 (1982) 155–171.

    MathSciNet  MATH  Google Scholar 

  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. L. BĂdescu, The projective plane blown up at a point as an ample divisor, Atti Accad. Ligure Scienze Lettere, 38 (1981) 3–7.

    MathSciNet  Google Scholar 

  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. C. BĂnicĂ-O. StĂnĂşilĂ, Algebraic Methods in the Global Theory of Complex Spaces, John Wiley, New York (1976).

    MATH  Google Scholar 

  8. E. Bombieri-D. Husemoller, Classification and embeddings of surfaces, Proc. Symp. Pure Math. 29 (1975) 329–420.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Buium, Weighted projective spaces as ample divisors, Revue Roum. Math. Pur. Appl. 26 (1981) 833–842.

    MathSciNet  MATH  Google Scholar 

  11. M. Demazure, Surfaces de Del Pezzo, in Springer Lecture Notes Math 777 (1980).

    Google Scholar 

  12. I. Dolgachev, Weighted projective varieties, in Springer Lecture Notes Math. 956 (1982).

    Google Scholar 

  13. L. de Fiore, S. Freni, Sulle varietà segate dagli iperpiani in varietà di Grassmann di indici qualunque, Preprint, Napoli (1980).

    Google Scholar 

  14. T. Fujita, Impossibility oriterion of being an ample divisor, J. Math. Soc. Japan 34 (1982) 355–363.

    Article  MathSciNet  MATH  Google Scholar 

  15. T. Fujita, Vector bundles on ample divisors, J. Math. Soc. Japan 33 (1981) 405–414.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  17. T. Fujita, On the structure of polarized manifolds with total deficiency one, I, J. Math. Soc. Japan 32 (1980) 709–725.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    MathSciNet  MATH  Google Scholar 

  19. A. Grothendieck-J. Dieudonné, Eléments de Géométrie Algebrique, Chap. II, III, IV, Publ. Math. IHES, Bures sur Yvette.

    Google Scholar 

  20. A. Grothendieck, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux, North Holland, Amsterdam (1968).

    MATH  Google Scholar 

  21. R. Hartshorne, Algebraic Geometry, Springer Verlag (1977).

    Google Scholar 

  22. R. Hartshorne, Curves with high self-intersection on algebraic surfaces, Publ. Math. IHES No. 36 (1969) 111–125.

    Google Scholar 

  23. R. Hartshorne, Topological conditions for smoothing algebraic singularities, Topology 13 (1974) 241–253.

    Article  MathSciNet  MATH  Google Scholar 

  24. F. Hidaka-K. Watanabe, Normal Gorenstein surfaces with ample anti-canonical divisor, Tokyo J. Math,, 4 (1981) 319–330.

    Article  MathSciNet  MATH  Google Scholar 

  25. P. Ionescu, Deformations of complete intersections, Revue Roum. Math. Pur. Appl. 25 (1980) 751–758.

    MathSciNet  MATH  Google Scholar 

  26. V.A. Iskovskih, Fano 3-folds, Math. USSR Izvest. 11 (1977) 485–527.

    Article  MathSciNet  Google Scholar 

  27. G. Kempf, Vanishing theorems for flag manifolds, Amer. J. Math. 98 (1976) 325–331.

    Article  MathSciNet  MATH  Google Scholar 

  28. S. Mori, On a generalization of complete intersections, J. Math. Kyoto Univ. 15 (1975) 619–646.

    MathSciNet  MATH  Google Scholar 

  29. D. Mumford, Varieties defined by quadratic equations, CIME (1969) 29–100 (Roma, Ediz. Cremonese).

    Google Scholar 

  30. D. Mumford, A remark on a paper of Schlessinger, Rice Univ. Studies 59 (1) (1973) 113–117.

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  32. H. Pinkham, Deformations of algebraic varieties with Gm-action, Astérisque 20, Société Math. de France (1974).

    Google Scholar 

  33. M. Schlessinger, On rigid singularities, Rice Univ. Studies 59 (1) (1973) 147–162.

    MathSciNet  MATH  Google Scholar 

  34. G. Scorza, Sopra una certa classe di varietà razionali, Rend. Circ. Matem. Palermo 28 (1909) 400–401.

    Article  MATH  Google Scholar 

  35. E. Sernesi, Small deformations of global complete intersections, Boll. Un. Matem. Ital. (4) 12 (1975) 138–146.

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  38. ***, Correspondence, Amer. J.Math. 79 (1957) 951–952 (=A. Weil, Oeuvres sc. II 555–556).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Dept. of Mathematics, Increst Bucharest, B-dul PĂcii 220, 79622, Bucharest, Rumania

    Lucian BĂdescu

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  1. Lucian BĂdescu
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Lucian Bădescu Dorin Popescu

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© 1984 Springer-Verlag

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BĂdescu, L. (1984). Hyperplane sections and deformations. In: Bădescu, L., Popescu, D. (eds) Algebraic Geometry Bucharest 1982. Lecture Notes in Mathematics, vol 1056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071767

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  • DOI: https://doi.org/10.1007/BFb0071767

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12930-1

  • Online ISBN: 978-3-540-38811-1

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